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A three term Polak-Ribière-Polyak conjugate gradient method close to the memoryless BFGS quasi-Newton method
Department of Mathematics and Computational Science, Huaihua University, Huaihua, Hunan 418008, China |
In this paper, we develop a three-term Polak-Ribière-Polyak conjugate gradient method, in which the search direction is close to the direction in the memoryless BFGS quasi-Newton method. The new scheme reduces to the standard Polak-Ribière-Polyak method when an exact line search is used. For any line search, the method satisfies the sufficient descent condition $g_{k}^{T}d_{k}≤ -{(1-\frac{1}{4}(1+\overline{t})^2})\|g_k\|^2$, where $\overline{t}∈[0,1)$ is a constant. The global convergence results of the new algorithm are established with suitable line search methods. Numerical results show that the proposed method is efficient for the unconstrained problems in the CUTEr library.
References:
[1] |
N. Andrei,
Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization, Bull. Malays. Math. Sci. Soc., 34 (2011), 319-330.
|
[2] |
S. Babaie-Kafaki and G. Reza,
A descent family of Dai-Liao conjugate gradient methods, Optim. Method. Softw., 21 (2013), 1-9.
doi: 10.1080/10556788.2013.833199. |
[3] |
I. Bongartz, A. Conn, N. Gould and P. Toint,
CUTE: constrained and unconstrained testing environments, ACM Trans. Math. Software, 21 (1995), 123-160.
doi: 10.1145/200979.201043. |
[4] |
Y. Dai and C. Kou,
A nonlinear conjugate gradient algorithm with an optimal property and an improved wolfe line search, SIAM J. Optim, 23 (2013), 296-320.
doi: 10.1137/100813026. |
[5] |
Y. Dai and L. Liao,
New conjugate conditions and related nonlinear conjugate gradient methods, Appl. Math. Optim., 43 (2001), 87-101.
doi: 10.1007/s002450010019. |
[6] |
Y. Dai and Y. Yuan,
A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (2000), 177-182.
doi: 10.1137/S1052623497318992. |
[7] |
Z. Dai and B. Tian,
Global convergence of some modified PRP nonlinear conjugate gradient methods, Optim. Lett., 5 (2011), 615-630.
doi: 10.1007/s11590-010-0224-8. |
[8] |
E. Dolan and J. Moré,
Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[9] |
R. Fletcher, Practical Method of Optimization, vol. 1: Unconstrained Optimization, John Wiley & Sons, New York, 1987. |
[10] |
R. Fletcher and C. Reeves,
Function minimization by conjugate gradients, Comput. J., 7 (1964), 149-154.
doi: 10.1093/comjnl/7.2.149. |
[11] |
J. Gilbert and J. Nocedal,
Global convergence properties of conjugate gradient methods for optimization, SIAM. J. Optim., 2 (1992), 21-42.
doi: 10.1137/0802003. |
[12] |
L. Grippo and S. Lucidi,
A globally convergent version of the Polak-Ribière-Polyak conjugate gradient method, Math. Program., 78 (1979), 375-391.
doi: 10.1007/BF02614362. |
[13] |
W. Hager and H. Zhang,
A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM J. Optim., 16 (2005), 170-192.
doi: 10.1137/030601880. |
[14] |
W. Hager and H. Zhang,
Algorithm 851: CG_ DESCENT, a conjugate gradient method with guaranteed descent, ACM Trans. Math. Software, 32 (2006), 113-137.
doi: 10.1145/1132973.1132979. |
[15] |
W. Hager and H. Zhang,
A survey of nonlinear conjugate gradient methods, Pac. J. Optim., 2 (2006), 35-58.
|
[16] |
M. Hestenes and E. Stiefel,
Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand., 49 (1952), 409-436.
doi: 10.6028/jres.049.044. |
[17] |
G. Li, C. Tang and Z. Wei,
New conjugacy condition and related new conjugate gradient methods for unconstrained optimization, J. Comput. Appl. Math., 202 (2007), 523-539.
doi: 10.1016/j.cam.2006.03.005. |
[18] |
M. Li, J. Liu and H. Feng,
The global convergence of a descent PRP conjugate gradient method, Comput. Appl. Math., 31 (2012), 59-83.
|
[19] |
D. Liu and J. Nocedal,
On the limited memory BFGS method for large-scale optimization, Math. Program., 45 (1989), 503-528.
doi: 10.1007/BF01589116. |
[20] |
Y. Liu and C. Storey,
Efficient generalized conjugate gradient algorithms, part 1: Theory, J. Optim. Theory Appl., 69 (1991), 177-182.
doi: 10.1007/BF00940464. |
[21] |
J. Nocedal,
Updating quasi-Newton matrices with limited storage, Math. Comput., 35 (1980), 773-782.
doi: 10.1090/S0025-5718-1980-0572855-7. |
[22] |
J. M. Perry, A class of conjugate gradient algorithms with a two-step variable-metric memory, Discussion Paper 269, Center for Mathematical Studies in Economics and Management Sciences, Northwestern University, Evanston, Illinois, 1977.
doi: 10.1287/opre.26.6.1073. |
[23] |
B. Polak and G. Ribière,
Note sur la convergence de directions conjuguées, Rev. Francaise Informat. Recherche Opertionelle, 3e Année, 16 (1969), 35-43.
|
[24] |
B. Polyak,
The conjugate gradient method in extreme problems, USSR Comp. Math. Math. Phys., 9 (1969), 94-112.
|
[25] |
M. Powell, Nonvonvex minimization calculations and the conjugate gradient method, in: Lecture Notes in Mathematics, vol. 1066, Springer-Verlag, Berlin, 1984.
doi: 10.1007/BFb0099521. |
[26] |
D. F. Shanno,
On the convergence of a new conjugate gradient algorithm, SIAM J. Numer. Anal., 15 (1978), 1247-1257.
doi: 10.1137/0715085. |
[27] |
D. Shanno,
Conjugate gradient methods with inexact searches, Math. Oper. Res., 3 (1978), 244-256.
doi: 10.1287/moor.3.3.244. |
[28] |
H. Yabe and M. Takano,
Global convergence properties of nonlinear conjugate gradient methods with modified secant condition, Comput. Optim. Appl., 28 (2004), 203-225.
doi: 10.1023/B:COAP.0000026885.81997.88. |
[29] |
G. Yu and L. Guan,
Modified PRP methods with sufficient desent property and their convergence properties, Acta Scientiarum Naturalium Universitatis Sunyatseni(Chinese), 45 (2006), 11-14.
|
[30] |
G. Yuan, Z. Meng and Y. Li,
A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations, J. Optimz. Theory App., 168 (2016), 129-152.
doi: 10.1007/s10957-015-0781-1. |
[31] |
G. Yuan, Z. Sheng, B. Wang, W. Hu and C. Li,
The global convergence of a modified BFGS method for nonconvex functions, J. Comput. Appl. Math., 327 (2018), 274-294.
doi: 10.1016/j.cam.2017.05.030. |
[32] |
G. Yuan, Z. Wei and G. Li,
A modified Polak-Ribiéere-Polyak conjugate gradient algorithm with nonmonotone line search for nonsmooth convex minimization, J. Comput. Appl. Math., 255 (2014), 86-96.
doi: 10.1007/s12190-015-0912-8. |
[33] |
G. Yuan, Z. Wei and X. Lu, Global convergence of the BFGS method and the PRP method for general functions under a modified weak Wolfe-Powell line search, Appl. Math. Model., 47 (2017), 811-825
doi: 10.1016/j.apm.2017.02.008. |
[34] |
G. Yuan,
Modified nonlinear conjugate gradient methods with sufficient descent property for largescale optimization problems, Optim. Lett., 3 (2009), 11-21.
doi: 10.1007/s11590-008-0086-5. |
[35] |
J. Zhang, N. Deng and L. Chen,
New quasi-newton equation and related methods for unconstrained optimization, J. Optim. Theory Appl., 102 (1999), 147-167.
doi: 10.1023/A:1021898630001. |
[36] |
L. Zhang,
New versions of the Hestenes-Stiefel nonlinear conjugate gradient method based on the secant condition for optimization, Comp. Appl. Math., 28 (2009), 1-23.
doi: 10.1590/S0101-82052009000100006. |
[37] |
L. Zhang, W. Zhou and D. Li,
A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal., 26 (2006), 629-640.
doi: 10.1093/imanum/drl016. |
[38] |
L. Zhang, W. Zhou and D. Li,
Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search, Numer. Math., 104 (2006), 561-572.
doi: 10.1007/s00211-006-0028-z. |
[39] |
G. Zoutendijk, Nonlinear programming, computational methods, in Integer and Nonlinear Programming (ed. J. Abadie), North-Holland, Amsterdam, 1970, 37-86. |
show all references
References:
[1] |
N. Andrei,
Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization, Bull. Malays. Math. Sci. Soc., 34 (2011), 319-330.
|
[2] |
S. Babaie-Kafaki and G. Reza,
A descent family of Dai-Liao conjugate gradient methods, Optim. Method. Softw., 21 (2013), 1-9.
doi: 10.1080/10556788.2013.833199. |
[3] |
I. Bongartz, A. Conn, N. Gould and P. Toint,
CUTE: constrained and unconstrained testing environments, ACM Trans. Math. Software, 21 (1995), 123-160.
doi: 10.1145/200979.201043. |
[4] |
Y. Dai and C. Kou,
A nonlinear conjugate gradient algorithm with an optimal property and an improved wolfe line search, SIAM J. Optim, 23 (2013), 296-320.
doi: 10.1137/100813026. |
[5] |
Y. Dai and L. Liao,
New conjugate conditions and related nonlinear conjugate gradient methods, Appl. Math. Optim., 43 (2001), 87-101.
doi: 10.1007/s002450010019. |
[6] |
Y. Dai and Y. Yuan,
A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (2000), 177-182.
doi: 10.1137/S1052623497318992. |
[7] |
Z. Dai and B. Tian,
Global convergence of some modified PRP nonlinear conjugate gradient methods, Optim. Lett., 5 (2011), 615-630.
doi: 10.1007/s11590-010-0224-8. |
[8] |
E. Dolan and J. Moré,
Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[9] |
R. Fletcher, Practical Method of Optimization, vol. 1: Unconstrained Optimization, John Wiley & Sons, New York, 1987. |
[10] |
R. Fletcher and C. Reeves,
Function minimization by conjugate gradients, Comput. J., 7 (1964), 149-154.
doi: 10.1093/comjnl/7.2.149. |
[11] |
J. Gilbert and J. Nocedal,
Global convergence properties of conjugate gradient methods for optimization, SIAM. J. Optim., 2 (1992), 21-42.
doi: 10.1137/0802003. |
[12] |
L. Grippo and S. Lucidi,
A globally convergent version of the Polak-Ribière-Polyak conjugate gradient method, Math. Program., 78 (1979), 375-391.
doi: 10.1007/BF02614362. |
[13] |
W. Hager and H. Zhang,
A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM J. Optim., 16 (2005), 170-192.
doi: 10.1137/030601880. |
[14] |
W. Hager and H. Zhang,
Algorithm 851: CG_ DESCENT, a conjugate gradient method with guaranteed descent, ACM Trans. Math. Software, 32 (2006), 113-137.
doi: 10.1145/1132973.1132979. |
[15] |
W. Hager and H. Zhang,
A survey of nonlinear conjugate gradient methods, Pac. J. Optim., 2 (2006), 35-58.
|
[16] |
M. Hestenes and E. Stiefel,
Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand., 49 (1952), 409-436.
doi: 10.6028/jres.049.044. |
[17] |
G. Li, C. Tang and Z. Wei,
New conjugacy condition and related new conjugate gradient methods for unconstrained optimization, J. Comput. Appl. Math., 202 (2007), 523-539.
doi: 10.1016/j.cam.2006.03.005. |
[18] |
M. Li, J. Liu and H. Feng,
The global convergence of a descent PRP conjugate gradient method, Comput. Appl. Math., 31 (2012), 59-83.
|
[19] |
D. Liu and J. Nocedal,
On the limited memory BFGS method for large-scale optimization, Math. Program., 45 (1989), 503-528.
doi: 10.1007/BF01589116. |
[20] |
Y. Liu and C. Storey,
Efficient generalized conjugate gradient algorithms, part 1: Theory, J. Optim. Theory Appl., 69 (1991), 177-182.
doi: 10.1007/BF00940464. |
[21] |
J. Nocedal,
Updating quasi-Newton matrices with limited storage, Math. Comput., 35 (1980), 773-782.
doi: 10.1090/S0025-5718-1980-0572855-7. |
[22] |
J. M. Perry, A class of conjugate gradient algorithms with a two-step variable-metric memory, Discussion Paper 269, Center for Mathematical Studies in Economics and Management Sciences, Northwestern University, Evanston, Illinois, 1977.
doi: 10.1287/opre.26.6.1073. |
[23] |
B. Polak and G. Ribière,
Note sur la convergence de directions conjuguées, Rev. Francaise Informat. Recherche Opertionelle, 3e Année, 16 (1969), 35-43.
|
[24] |
B. Polyak,
The conjugate gradient method in extreme problems, USSR Comp. Math. Math. Phys., 9 (1969), 94-112.
|
[25] |
M. Powell, Nonvonvex minimization calculations and the conjugate gradient method, in: Lecture Notes in Mathematics, vol. 1066, Springer-Verlag, Berlin, 1984.
doi: 10.1007/BFb0099521. |
[26] |
D. F. Shanno,
On the convergence of a new conjugate gradient algorithm, SIAM J. Numer. Anal., 15 (1978), 1247-1257.
doi: 10.1137/0715085. |
[27] |
D. Shanno,
Conjugate gradient methods with inexact searches, Math. Oper. Res., 3 (1978), 244-256.
doi: 10.1287/moor.3.3.244. |
[28] |
H. Yabe and M. Takano,
Global convergence properties of nonlinear conjugate gradient methods with modified secant condition, Comput. Optim. Appl., 28 (2004), 203-225.
doi: 10.1023/B:COAP.0000026885.81997.88. |
[29] |
G. Yu and L. Guan,
Modified PRP methods with sufficient desent property and their convergence properties, Acta Scientiarum Naturalium Universitatis Sunyatseni(Chinese), 45 (2006), 11-14.
|
[30] |
G. Yuan, Z. Meng and Y. Li,
A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations, J. Optimz. Theory App., 168 (2016), 129-152.
doi: 10.1007/s10957-015-0781-1. |
[31] |
G. Yuan, Z. Sheng, B. Wang, W. Hu and C. Li,
The global convergence of a modified BFGS method for nonconvex functions, J. Comput. Appl. Math., 327 (2018), 274-294.
doi: 10.1016/j.cam.2017.05.030. |
[32] |
G. Yuan, Z. Wei and G. Li,
A modified Polak-Ribiéere-Polyak conjugate gradient algorithm with nonmonotone line search for nonsmooth convex minimization, J. Comput. Appl. Math., 255 (2014), 86-96.
doi: 10.1007/s12190-015-0912-8. |
[33] |
G. Yuan, Z. Wei and X. Lu, Global convergence of the BFGS method and the PRP method for general functions under a modified weak Wolfe-Powell line search, Appl. Math. Model., 47 (2017), 811-825
doi: 10.1016/j.apm.2017.02.008. |
[34] |
G. Yuan,
Modified nonlinear conjugate gradient methods with sufficient descent property for largescale optimization problems, Optim. Lett., 3 (2009), 11-21.
doi: 10.1007/s11590-008-0086-5. |
[35] |
J. Zhang, N. Deng and L. Chen,
New quasi-newton equation and related methods for unconstrained optimization, J. Optim. Theory Appl., 102 (1999), 147-167.
doi: 10.1023/A:1021898630001. |
[36] |
L. Zhang,
New versions of the Hestenes-Stiefel nonlinear conjugate gradient method based on the secant condition for optimization, Comp. Appl. Math., 28 (2009), 1-23.
doi: 10.1590/S0101-82052009000100006. |
[37] |
L. Zhang, W. Zhou and D. Li,
A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal., 26 (2006), 629-640.
doi: 10.1093/imanum/drl016. |
[38] |
L. Zhang, W. Zhou and D. Li,
Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search, Numer. Math., 104 (2006), 561-572.
doi: 10.1007/s00211-006-0028-z. |
[39] |
G. Zoutendijk, Nonlinear programming, computational methods, in Integer and Nonlinear Programming (ed. J. Abadie), North-Holland, Amsterdam, 1970, 37-86. |


No. | Prob | Dim | No. | Prob | Dim | No. | Prob | Dim | ||
No. | Prob | Dim | No. | Prob | Dim | No. | Prob | Dim | ||
1 | ARGLINA | 100 | 52 | DIXMAANK | 1500 | 103 | NONDQUAR | 1000 | ||
2 | ARGLINA | 200 | 53 | DIXMAANL | 300 | 104 | NONMSQRT | 100 | ||
3 | ARGLINB | 100 | 54 | DIXMAANL | 1500 | 105 | OSCIPATH | 100 | ||
4 | ARGLINB | 200 | 55 | DIXON3DQ | 100 | 106 | OSCIPATH | 500 | ||
5 | ARGLINC | 50 | 56 | DIXON3DQ | 1000 | 107 | PENALTY1 | 50 | ||
6 | ARGLINC | 200 | 57 | DQDRTIC | 1000 | 108 | PENALTY1 | 100 | ||
7 | ARWHEAD | 100 | 58 | DQDRTIC | 5000 | 109 | PENALTY2 | 100 | ||
8 | ARWHEAD | 1000 | 59 | DQRTIC | 500 | 110 | PENALTY2 | 200 | ||
9 | BDQRTIC | 100 | 60 | DQRTIC | 1000 | 111 | PENALTY3 | 50 | ||
10 | BDQRTIC | 500 | 61 | EDENSCH | 2000 | 112 | PENALTY3 | 100 | ||
11 | BDQRTIC | 1000 | 62 | EG2 | 1000 | 113 | POWELLSG | 100 | ||
12 | BOX | 100 | 63 | ENGVAL1 | 1000 | 114 | POWELLSG | 10000 | ||
13 | BOX | 1000 | 64 | ENGVAL1 | 5000 | 115 | POWER | 5000 | ||
14 | BROWNAL | 200 | 65 | ERRINROS | 50 | 116 | POWER | 10000 | ||
15 | BROYDN7D | 100 | 66 | EXTROSNB | 100 | 117 | QUARTC | 100 | ||
16 | BROYDN7D | 10000 | 67 | EXTROSNB | 1000 | 118 | QUARTC | 10000 | ||
17 | BRYBND | 100 | 68 | FLETCBV2 | 5000 | 119 | SCHMVETT | 100 | ||
18 | BRYBND | 500 | 69 | FLETCBV2 | 10000 | 120 | SCHMVETT | 10000 | ||
19 | CHAINWOO | 1000 | 70 | FLETCHBV | 100 | 121 | SCOSINE | 100 | ||
20 | COSINE | 1000 | 71 | FLETCHCR | 1000 | 122 | SCURLY10 | 100 | ||
21 | COSINE | 10000 | 72 | FMINSRF2 | 5625 | 123 | SCURLY20 | 100 | ||
22 | CRAGGLVY | 1000 | 73 | FMINSRF2 | 10000 | 124 | SCURLY30 | 100 | ||
23 | CRAGGLVY | 5000 | 74 | FMINSURF | 121 | 125 | SENSORS | 100 | ||
24 | CURLY10 | 100 | 75 | FMINSURF | 10000 | 126 | SINQUAD | 500 | ||
25 | CURLY10 | 1000 | 76 | FREUROTH | 100 | 127 | SINQUAD | 10000 | ||
26 | CURLY20 | 100 | 77 | FREUROTH | 5000 | 128 | SPARSINE | 50 | ||
27 | CURLY20 | 1000 | 78 | GENHUMPS | 1000 | 129 | SPARSINE | 1000 | ||
28 | CURLY30 | 100 | 79 | GENHUMPS | 5000 | 130 | SPARSQUR | 5000 | ||
29 | CURLY30 | 1000 | 80 | GENROSE | 100 | 131 | SPARSQUR | 10000 | ||
30 | DECONVU | 61 | 81 | GENROSE | 500 | 132 | SPMSRTLS | 4999 | ||
31 | DIXMAANA | 3000 | 82 | HILBERTA | 10 | 133 | SPMSRTLS | 10000 | ||
32 | DIXMAANA | 9000 | 83 | HILBERTB | 50 | 134 | SROSENBR | 100 | ||
33 | DIXMAANB | 300 | 84 | HYDC20LS | 99 | 135 | SROSENBR | 5000 | ||
34 | DIXMAANB | 9000 | 85 | LIARWHD | 100 | 136 | SROSENBR | 10000 | ||
35 | DIXMAANC | 90 | 86 | LIARWHD | 10000 | 137 | TESTQUAD | 1000 | ||
36 | DIXMAANC | 9000 | 87 | MANCINO | 50 | 138 | TESTQUAD | 5000 | ||
37 | DIXMAAND | 300 | 88 | MANCINO | 100 | 139 | TOINTGOR | 50 | ||
38 | DIXMAAND | 1500 | 89 | MODBEALE | 200 | 140 | TOINTGSS | 100 | ||
39 | DIXMAANE | 90 | 90 | MODBEALE | 2000 | 141 | TOINTGSS | 1000 | ||
40 | DIXMAANE | 1500 | 91 | MOREBV | 50 | 142 | TOINTPSP | 50 | ||
41 | DIXMAANF | 1500 | 92 | MOREBV | 500 | 143 | TOINTQOR | 50 | ||
42 | DIXMAANF | 9000 | 93 | MSQRTALS | 100 | 144 | TQUARTIC | 500 | ||
43 | DIXMAANG | 90 | 94 | MSQRTALS | 529 | 145 | TQUARTIC | 5000 | ||
44 | DIXMAANG | 300 | 95 | MSQRTBLS | 100 | 146 | TRIDIA | 100 | ||
45 | DIXMAANH | 3000 | 96 | MSQRTBLS | 1024 | 147 | TRIDIA | 1000 | ||
46 | DIXMAANH | 9000 | 97 | NONCVXU2 | 1000 | 148 | VARDIM | 50 | ||
47 | DIXMAANI | 300 | 98 | NONCVXU2 | 10000 | 149 | VARDIM | 100 | ||
48 | DIXMAANI | 1500 | 99 | NONCVXUN | 100 | 150 | VAREIGVL | 1000 | ||
49 | DIXMAANJ | 300 | 100 | NONDIA | 5000 | 151 | VAREIGVL | 5000 | ||
50 | DIXMAANJ | 1500 | 101 | NONDIA | 10000 | 152 | WOODS | 4000 | ||
51 | DIXMAANK | 300 | 102 | NONDQUAR | 500 | 153 | WOODS | 10000 |
No. | Prob | Dim | No. | Prob | Dim | No. | Prob | Dim | ||
No. | Prob | Dim | No. | Prob | Dim | No. | Prob | Dim | ||
1 | ARGLINA | 100 | 52 | DIXMAANK | 1500 | 103 | NONDQUAR | 1000 | ||
2 | ARGLINA | 200 | 53 | DIXMAANL | 300 | 104 | NONMSQRT | 100 | ||
3 | ARGLINB | 100 | 54 | DIXMAANL | 1500 | 105 | OSCIPATH | 100 | ||
4 | ARGLINB | 200 | 55 | DIXON3DQ | 100 | 106 | OSCIPATH | 500 | ||
5 | ARGLINC | 50 | 56 | DIXON3DQ | 1000 | 107 | PENALTY1 | 50 | ||
6 | ARGLINC | 200 | 57 | DQDRTIC | 1000 | 108 | PENALTY1 | 100 | ||
7 | ARWHEAD | 100 | 58 | DQDRTIC | 5000 | 109 | PENALTY2 | 100 | ||
8 | ARWHEAD | 1000 | 59 | DQRTIC | 500 | 110 | PENALTY2 | 200 | ||
9 | BDQRTIC | 100 | 60 | DQRTIC | 1000 | 111 | PENALTY3 | 50 | ||
10 | BDQRTIC | 500 | 61 | EDENSCH | 2000 | 112 | PENALTY3 | 100 | ||
11 | BDQRTIC | 1000 | 62 | EG2 | 1000 | 113 | POWELLSG | 100 | ||
12 | BOX | 100 | 63 | ENGVAL1 | 1000 | 114 | POWELLSG | 10000 | ||
13 | BOX | 1000 | 64 | ENGVAL1 | 5000 | 115 | POWER | 5000 | ||
14 | BROWNAL | 200 | 65 | ERRINROS | 50 | 116 | POWER | 10000 | ||
15 | BROYDN7D | 100 | 66 | EXTROSNB | 100 | 117 | QUARTC | 100 | ||
16 | BROYDN7D | 10000 | 67 | EXTROSNB | 1000 | 118 | QUARTC | 10000 | ||
17 | BRYBND | 100 | 68 | FLETCBV2 | 5000 | 119 | SCHMVETT | 100 | ||
18 | BRYBND | 500 | 69 | FLETCBV2 | 10000 | 120 | SCHMVETT | 10000 | ||
19 | CHAINWOO | 1000 | 70 | FLETCHBV | 100 | 121 | SCOSINE | 100 | ||
20 | COSINE | 1000 | 71 | FLETCHCR | 1000 | 122 | SCURLY10 | 100 | ||
21 | COSINE | 10000 | 72 | FMINSRF2 | 5625 | 123 | SCURLY20 | 100 | ||
22 | CRAGGLVY | 1000 | 73 | FMINSRF2 | 10000 | 124 | SCURLY30 | 100 | ||
23 | CRAGGLVY | 5000 | 74 | FMINSURF | 121 | 125 | SENSORS | 100 | ||
24 | CURLY10 | 100 | 75 | FMINSURF | 10000 | 126 | SINQUAD | 500 | ||
25 | CURLY10 | 1000 | 76 | FREUROTH | 100 | 127 | SINQUAD | 10000 | ||
26 | CURLY20 | 100 | 77 | FREUROTH | 5000 | 128 | SPARSINE | 50 | ||
27 | CURLY20 | 1000 | 78 | GENHUMPS | 1000 | 129 | SPARSINE | 1000 | ||
28 | CURLY30 | 100 | 79 | GENHUMPS | 5000 | 130 | SPARSQUR | 5000 | ||
29 | CURLY30 | 1000 | 80 | GENROSE | 100 | 131 | SPARSQUR | 10000 | ||
30 | DECONVU | 61 | 81 | GENROSE | 500 | 132 | SPMSRTLS | 4999 | ||
31 | DIXMAANA | 3000 | 82 | HILBERTA | 10 | 133 | SPMSRTLS | 10000 | ||
32 | DIXMAANA | 9000 | 83 | HILBERTB | 50 | 134 | SROSENBR | 100 | ||
33 | DIXMAANB | 300 | 84 | HYDC20LS | 99 | 135 | SROSENBR | 5000 | ||
34 | DIXMAANB | 9000 | 85 | LIARWHD | 100 | 136 | SROSENBR | 10000 | ||
35 | DIXMAANC | 90 | 86 | LIARWHD | 10000 | 137 | TESTQUAD | 1000 | ||
36 | DIXMAANC | 9000 | 87 | MANCINO | 50 | 138 | TESTQUAD | 5000 | ||
37 | DIXMAAND | 300 | 88 | MANCINO | 100 | 139 | TOINTGOR | 50 | ||
38 | DIXMAAND | 1500 | 89 | MODBEALE | 200 | 140 | TOINTGSS | 100 | ||
39 | DIXMAANE | 90 | 90 | MODBEALE | 2000 | 141 | TOINTGSS | 1000 | ||
40 | DIXMAANE | 1500 | 91 | MOREBV | 50 | 142 | TOINTPSP | 50 | ||
41 | DIXMAANF | 1500 | 92 | MOREBV | 500 | 143 | TOINTQOR | 50 | ||
42 | DIXMAANF | 9000 | 93 | MSQRTALS | 100 | 144 | TQUARTIC | 500 | ||
43 | DIXMAANG | 90 | 94 | MSQRTALS | 529 | 145 | TQUARTIC | 5000 | ||
44 | DIXMAANG | 300 | 95 | MSQRTBLS | 100 | 146 | TRIDIA | 100 | ||
45 | DIXMAANH | 3000 | 96 | MSQRTBLS | 1024 | 147 | TRIDIA | 1000 | ||
46 | DIXMAANH | 9000 | 97 | NONCVXU2 | 1000 | 148 | VARDIM | 50 | ||
47 | DIXMAANI | 300 | 98 | NONCVXU2 | 10000 | 149 | VARDIM | 100 | ||
48 | DIXMAANI | 1500 | 99 | NONCVXUN | 100 | 150 | VAREIGVL | 1000 | ||
49 | DIXMAANJ | 300 | 100 | NONDIA | 5000 | 151 | VAREIGVL | 5000 | ||
50 | DIXMAANJ | 1500 | 101 | NONDIA | 10000 | 152 | WOODS | 4000 | ||
51 | DIXMAANK | 300 | 102 | NONDQUAR | 500 | 153 | WOODS | 10000 |
CG_DESCENT method | MPRP method | NPRP+ method | |
No. | Iter/Nf/Ng/Time | Iter/Nf/Ng/Time | Iter/Nf/Ng/Time |
1 | 1/3/2/0.001 | 1/3/2/0.001 | 1/3/2/0 |
2 | 1/3/2/0.002 | 1/3/2/0.002 | 1/3/2/0.001 |
3 | 4/8/7/0.001 | 5/10/10/0.001 | 5/10/10/0.000999 |
4 | 9/16/20/0.005999 | 7/13/15/0.004999 | 7/13/15/0.004999 |
5 | 3/7/5/0 | 3/7/5/0 | 3/7/5/0 |
6 | 8/14/17/0.003999 | 5/11/11/0.003 | 5/11/11/0.004 |
7 | 9/21/15/0 | 12/27/19/0.000999 | 9/21/15/0 |
8 | 10/24/16/0.002 | 9/21/14/0.002 | 8/21/16/0.002 |
9 | 131/255/180/0.003999 | 126/245/164/0.001999 | 101/195/173/0.003 |
10 | 375/765/503/0.027996 | 510/890/740/0.039994 | 490/700/1025/0.046993 |
11 | 531/1100/718/0.078988 | 405/861/589/0.06499 | 238/533/540/0.052992 |
12 | 15/31/23/0.001 | 11/24/16/0.001 | 12/25/17/0.001 |
13 | 13/34/28/0.002999 | 36/60/77/0.007999 | 18/43/33/0.004999 |
14 | 4/9/6/0.001 | 15/31/21/0.003999 | 18/37/26/0.004 |
15 | 82/157/91/0.006999 | 90/171/101/0.005 | 79/152/87/0.004 |
16 | 2909/5808/2925/15.238 | 2819/5621/2840/15.294 | 2794/5573/2811/15.206 |
17 | 113/227/114/0.002 | 112/225/114/0.002 | 106/213/107/0.001999 |
18 | 37/75/38/0.003 | 27/55/28/0.003999 | 29/60/31/0.002999 |
19 | 448/834/531/0.061991 | 436/770/577/0.062991 | 4517/8797/4945/0.61991 |
20 | 12/28/24/0.003999 | 10/25/21/0.003999 | 11/27/22/0.003 |
21 | 12/32/28/0.038994 | 11/27/25/0.033995 | 10/25/21/0.029996 |
22 | 103/185/128/0.041994 | 122/230/159/0.050992 | 108/194/133/0.043993 |
23 | 110/200/139/0.22697 | 132/252/184/0.30595 | 99/179/131/0.24196 |
24 | 991/1777/1387/0.010999 | 1018/1825/1492/0.009999 | 936/1718/1286/0.008999 |
25 | 8654/13686/12760/0.84087 | 9755/14820/15245/0.97685 | 8911/13925/13444/0.94286 |
26 | 875/1612/1299/0.015998 | 852/1590/1249/0.016997 | 894/1658/1277/0.014998 |
27 | 9816/15450/15254/1.3928 | 10806/16627/17405/1.5678 | 9776/15443/15149/1.4718 |
28 | 986/1857/1447/0.018997 | 978/1828/1484/0.017997 | 989/1833/1419/0.016998 |
29 | 9832/15701/15229/1.7937 | 9824/15661/15379/1.8267 | 10778/16930/17516/2.2757 |
30 | 337/676/339/0.005999 | 385/773/390/0.006999 | 395/793/400/0.007998 |
31 | 9/19/10/0.003999 | 7/15/8/0.004999 | 7/15/8/0.004 |
32 | 9/19/10/0.008999 | 7/15/8/0.008999 | 7/15/8/0.006999 |
33 | 9/19/10/0.001 | 8/17/9/0.001 | 8/17/9/0.000999 |
34 | 9/19/10/0.008999 | 8/17/9/0.007999 | 8/17/9/0.007998 |
35 | 10/21/11/0.001 | 9/19/10/0.001 | 9/19/10/0.000999 |
36 | 10/21/11/0.009999 | 9/19/10/0.008998 | 9/19/10/0.008999 |
37 | 12/25/13/0.000999 | 11/23/12/0.001 | 11/23/12/0.001 |
38 | 12/25/13/0.001999 | 11/23/12/0.001999 | 11/23/12/0.001999 |
39 | 48/97/49/0.000999 | 49/99/50/0.001 | 48/97/49/0.000999 |
40 | 167/335/168/0.028996 | 168/337/169/0.024996 | 169/339/170/0.023996 |
41 | 133/267/134/0.019997 | 129/259/130/0.018997 | 127/255/128/0.018997 |
42 | 269/539/270/0.24496 | 265/531/266/0.24396 | 263/527/264/0.25996 |
43 | 54/109/55/0.000999 | 52/105/53/0.001 | 52/105/53/0.000999 |
44 | 83/167/84/0.002999 | 81/163/82/0.003 | 79/159/80/0.002 |
45 | 167/335/168/0.057992 | 169/339/170/0.058991 | 164/329/165/0.054992 |
46 | 263/527/264/0.23896 | 266/533/267/0.24796 | 256/513/257/0.23396 |
47 | 1046/2093/1047/0.030995 | 1057/2115/1058/0.032995 | 938/1877/939/0.027996 |
48 | 2926/5853/2927/0.43093 | 2914/5829/2915/0.43593 | 2918/5837/2919/0.42993 |
49 | 635/1271/636/0.018997 | 607/1215/608/0.018997 | 599/1199/600/0.018997 |
50 | 1467/2935/1468/0.20897 | 1478/2957/1479/0.21497 | 1413/2827/1414/0.21397 |
51 | 606/1213/607/0.019997 | 602/1205/603/0.022997 | 481/963/482/0.013998 |
52 | 1434/2869/1435/0.21897 | 1413/2827/1414/0.20497 | 1387/2775/1388/0.28396 |
53 | 596/1193/597/0.020997 | 604/1209/605/0.018997 | 388/777/389/0.016998 |
54 | 1374/2749/1375/0.20497 | 1424/2849/1425/0.20697 | 1356/2713/1357/0.20697 |
55 | 200/401/202/0.001999 | 200/401/202/0.001999 | 200/401/202/0.001999 |
56 | 1000/2001/1002/0.048992 | 1000/2001/1002/0.06199 | 1000/2001/1002/0.050992 |
57 | 7/15/8/0.002 | 7/15/8/0.002 | 6/13/7/0.001999 |
58 | 7/15/8/0.004 | 7/15/8/0.004999 | 7/15/8/0.003999 |
59 | 28/57/29/0.001 | 27/55/28/0.001 | 27/55/28/0.001 |
60 | 29/59/30/0.000999 | 29/59/30/0.002 | 29/59/30/0.002 |
61 | 32/59/40/0.010999 | 32/60/45/0.009998 | 31/56/39/0.011998 |
62 | 4/9/6/0.001 | 4/9/6/0.001 | 4/9/6/0.001 |
63 | 26/48/33/0.003 | 26/49/33/0.003 | 22/42/28/0.002999 |
64 | 27/50/40/0.016997 | 25/44/34/0.014998 | 23/42/30/0.013998 |
65 | 1151/2285/1599/0.008998 | 1150/2270/1564/0.006998 | 1708/3414/2234/0.013998 |
66 | 5481/11373/6023/0.041993 | 5510/11246/5845/0.041994 | 5906/12296/6550/0.045993 |
67 | 6354/13073/6816/0.47393 | 7741/15623/7929/0.54592 | 7866/16031/8277/0.61791 |
68 | 0/1/1/0.001999 | 0/1/1/0.001999 | 0/1/1/0.001 |
69 | 0/1/1/0.002999 | 0/1/1/0.003 | 0/1/1/0.002 |
70 | F/F/F/F | F/F/F/F | F/F/F/F |
71 | 6604/13682/7147/0.6859 | 4310/8650/4348/0.43493 | 6879/14253/7386/0.74789 |
72 | 368/739/371/0.25896 | 305/611/306/0.20897 | 395/792/397/0.28096 |
73 | 434/869/435/0.54392 | 375/752/377/0.53992 | 460/922/462/0.60891 |
74 | 88/178/90/0.001999 | 92/186/94/0.001999 | 80/162/82/0.002 |
75 | 603/1209/606/0.85987 | 454/910/456/0.6459 | 655/1311/656/0.96185 |
76 | 52/103/80/0.000999 | 107/205/145/0.003 | 36/72/65/0.001 |
77 | 53/107/80/0.047993 | 49/97/74/0.044993 | 33/68/56/0.032995 |
78 | 2720/5482/2769/1.2288 | 1895/4067/2224/0.93486 | 2964/5978/3028/1.3378 |
79 | 6653/13399/6765/14.238 | 5844/12355/6649/12.715 | 7015/14081/7077/14.59 |
80 | 297/631/344/0.005999 | 297/622/337/0.003 | 319/677/367/0.005999 |
81 | 1257/2553/1321/0.070989 | 1094/2231/1154/0.054992 | 1183/2404/1237/0.06899 |
82 | 7/15/10/0.001 | 7/15/10/0 | 7/15/10/0.001 |
83 | 5/11/6/0.001 | 5/11/6/0.001 | 5/11/6/0.001 |
84 | F/F/F/F | F/F/F/F | F/F/F/F |
85 | 18/37/19/0.000999 | 19/40/23/0.001 | 19/39/23/0 |
86 | 23/54/38/0.031995 | 23/50/32/0.028996 | 24/50/30/0.026996 |
87 | 9/19/10/0.013998 | 9/19/10/0.011998 | 10/21/11/0.012998 |
88 | 11/23/12/0.057991 | 10/21/11/0.052991 | 10/21/11/0.052992 |
89 | 334/684/430/0.025996 | 453/910/511/0.027996 | 249/501/306/0.015998 |
90 | 1085/2106/1395/0.75888 | F/F/F/F | 561/1137/584/0.34195 |
91 | 5640/11281/5776/0.024996 | 7051/14103/7209/0.031995 | 4262/8525/4365/0.018997 |
92 | 502/1005/503/0.026996 | 489/979/490/0.020997 | 484/969/485/0.019997 |
93 | 284/577/295/0.012998 | 282/573/293/0.008999 | 282/573/293/0.008998 |
94 | 4753/9513/4762/1.8517 | 5342/10691/5351/1.9547 | 5242/10491/5251/1.9357 |
95 | 356/717/362/0.011998 | 355/716/363/0.017996 | 356/718/364/0.010999 |
96 | 2309/4624/2316/2.6026 | 2209/4425/2218/2.4486 | 2227/4460/2234/2.4826 |
97 | 1801/3346/2059/0.49393 | 1968/3821/2085/0.48993 | 1913/3704/2037/0.47193 |
98 | 9063/17431/9760/22.829 | 8928/17306/9480/22.166 | 8989/17216/9753/23.235 |
99 | 168/329/179/0.005998 | 150/298/154/0.004999 | 160/315/173/0.005999 |
100 | 10/23/16/0.006999 | 10/37/32/0.010998 | 9/31/25/0.008999 |
101 | 8/26/22/0.014997 | 9/22/14/0.011999 | 7/16/10/0.008999 |
102 | 4004/8014/4257/0.11298 | 3540/7087/3693/0.10298 | 1758/3522/1999/0.06199 |
103 | 3027/6061/3162/0.21297 | 2014/4032/2071/0.11298 | 1705/3414/1878/0.10898 |
104 | F/F/F/F | F/F/F/F | F/F/F/F |
105 | 13/26/15/0.001 | 13/28/15/0 | 13/28/15/0 |
106 | 14/28/16/0.001 | 15/31/18/0.002 | 14/29/15/0.001 |
107 | 44/121/84/0.000999 | 47/140/101/0.001 | 41/106/73/0.000999 |
108 | 44/134/98/0.001 | 49/126/87/0.001 | 44/123/87/0.000999 |
109 | 84/141/143/0.009999 | 97/160/158/0.009998 | 81/140/132/0.010999 |
110 | 200/235/367/0.044993 | 211/245/395/0.042994 | 191/224/353/0.038994 |
111 | 70/174/124/0.025997 | 95/214/150/0.024996 | 70/167/118/0.019997 |
112 | F/F/F/F | F/F/F/F | 78/175/124/0.080988 |
113 | 103/214/121/0.001 | 102/206/112/0.000999 | 191/383/237/0.001999 |
114 | 224/461/272/0.11898 | 115/232/124/0.059991 | 201/403/240/0.10798 |
115 | 258/517/259/0.043993 | 762/1525/763/0.13298 | 372/745/373/0.06499 |
116 | 369/739/370/0.12398 | 1116/2233/1117/0.40794 | 473/947/474/0.17397 |
117 | 24/49/25/0.001 | 23/47/24/0.001 | 23/47/24/0.000999 |
118 | 35/71/36/0.016998 | 34/69/35/0.016998 | 34/69/35/0.015997 |
119 | 46/82/58/0.002999 | 44/79/55/0.003 | 44/78/56/0.003 |
120 | 39/65/54/0.26096 | 41/69/56/0.27796 | 41/69/56/0.27096 |
121 | F/F/F/F | F/F/F/F | F/F/F/F |
122 | F/F/F/F | F/F/F/F | F/F/F/F |
123 | F/F/F/F | F/F/F/F | F/F/F/F |
124 | F/F/F/F | F/F/F/F | F/F/F/F |
125 | 24/57/43/0.19897 | 32/72/57/0.25396 | 22/49/32/0.15398 |
126 | 44/108/92/0.010998 | 54/125/104/0.010998 | 43/115/95/0.009999 |
127 | 88/166/179/0.35795 | 68/166/142/0.27996 | 37/95/83/0.16198 |
128 | 164/331/168/0.003 | 185/375/192/0.003 | 165/333/170/0.002999 |
129 | 4499/8999/4500/1.1628 | 5259/10519/5260/1.3568 | 4737/9475/4738/1.2478 |
130 | 21/43/22/0.016998 | 21/43/22/0.016998 | 21/43/22/0.017998 |
131 | 22/45/23/0.039994 | 22/45/23/0.038994 | 22/45/23/0.038994 |
132 | 218/443/227/0.15398 | 206/419/215/0.14698 | 201/409/210/0.14298 |
133 | 225/457/234/0.33295 | 214/435/223/0.33495 | 207/421/216/0.30895 |
134 | 11/24/14/0.001 | 10/22/13/0.001 | 11/24/15/0.001 |
135 | 12/26/16/0.004998 | 10/22/13/0.002999 | 11/24/15/0.003999 |
136 | 12/26/17/0.008999 | 10/22/13/0.006999 | 11/24/15/0.007999 |
137 | 870/1741/871/0.041994 | 856/1713/857/0.033995 | 855/1711/856/0.033995 |
138 | 1641/3283/1642/0.30795 | 1728/3457/1729/0.33695 | 1682/3365/1683/0.32395 |
139 | 122/221/153/0.002999 | 120/221/149/0.001999 | 121/223/150/0.001999 |
140 | 13/26/15/0.000999 | 14/28/16/0.001 | 14/28/16/0.000999 |
141 | 6/13/7/0.003 | 6/13/7/0.003 | 6/13/7/0.002999 |
142 | 156/325/213/0.001 | 130/270/191/0.001 | 137/282/194/0.002 |
143 | 32/61/41/0.001 | 32/60/40/0 | 31/58/37/0.000999 |
144 | 25/62/42/0.002 | 20/76/63/0.002 | 18/45/33/0.002 |
145 | 22/54/39/0.015998 | 18/71/61/0.016997 | 23/72/56/0.014998 |
146 | 92/185/93/0.000999 | 92/185/93/0.001 | 91/183/92/0.000999 |
147 | 338/677/339/0.017997 | 339/679/340/0.016997 | 338/677/339/0.016996 |
148 | 21/43/22/0.001 | 21/43/22/0 | 21/43/22/0 |
149 | 25/51/26/0.001 | 25/51/26/0.001 | 25/51/26/0.001 |
150 | 93/243/150/0.026996 | 101/271/170/0.024996 | 81/214/133/0.019997 |
151 | 119/303/184/0.15498 | 108/291/184/0.14598 | 106/285/184/0.13598 |
152 | 268/554/301/0.082988 | 271/562/303/0.084987 | 157/355/225/0.057991 |
153 | 241/521/308/0.21097 | 208/462/286/0.18797 | 161/358/228/0.17597 |
CG_DESCENT method | MPRP method | NPRP+ method | |
No. | Iter/Nf/Ng/Time | Iter/Nf/Ng/Time | Iter/Nf/Ng/Time |
1 | 1/3/2/0.001 | 1/3/2/0.001 | 1/3/2/0 |
2 | 1/3/2/0.002 | 1/3/2/0.002 | 1/3/2/0.001 |
3 | 4/8/7/0.001 | 5/10/10/0.001 | 5/10/10/0.000999 |
4 | 9/16/20/0.005999 | 7/13/15/0.004999 | 7/13/15/0.004999 |
5 | 3/7/5/0 | 3/7/5/0 | 3/7/5/0 |
6 | 8/14/17/0.003999 | 5/11/11/0.003 | 5/11/11/0.004 |
7 | 9/21/15/0 | 12/27/19/0.000999 | 9/21/15/0 |
8 | 10/24/16/0.002 | 9/21/14/0.002 | 8/21/16/0.002 |
9 | 131/255/180/0.003999 | 126/245/164/0.001999 | 101/195/173/0.003 |
10 | 375/765/503/0.027996 | 510/890/740/0.039994 | 490/700/1025/0.046993 |
11 | 531/1100/718/0.078988 | 405/861/589/0.06499 | 238/533/540/0.052992 |
12 | 15/31/23/0.001 | 11/24/16/0.001 | 12/25/17/0.001 |
13 | 13/34/28/0.002999 | 36/60/77/0.007999 | 18/43/33/0.004999 |
14 | 4/9/6/0.001 | 15/31/21/0.003999 | 18/37/26/0.004 |
15 | 82/157/91/0.006999 | 90/171/101/0.005 | 79/152/87/0.004 |
16 | 2909/5808/2925/15.238 | 2819/5621/2840/15.294 | 2794/5573/2811/15.206 |
17 | 113/227/114/0.002 | 112/225/114/0.002 | 106/213/107/0.001999 |
18 | 37/75/38/0.003 | 27/55/28/0.003999 | 29/60/31/0.002999 |
19 | 448/834/531/0.061991 | 436/770/577/0.062991 | 4517/8797/4945/0.61991 |
20 | 12/28/24/0.003999 | 10/25/21/0.003999 | 11/27/22/0.003 |
21 | 12/32/28/0.038994 | 11/27/25/0.033995 | 10/25/21/0.029996 |
22 | 103/185/128/0.041994 | 122/230/159/0.050992 | 108/194/133/0.043993 |
23 | 110/200/139/0.22697 | 132/252/184/0.30595 | 99/179/131/0.24196 |
24 | 991/1777/1387/0.010999 | 1018/1825/1492/0.009999 | 936/1718/1286/0.008999 |
25 | 8654/13686/12760/0.84087 | 9755/14820/15245/0.97685 | 8911/13925/13444/0.94286 |
26 | 875/1612/1299/0.015998 | 852/1590/1249/0.016997 | 894/1658/1277/0.014998 |
27 | 9816/15450/15254/1.3928 | 10806/16627/17405/1.5678 | 9776/15443/15149/1.4718 |
28 | 986/1857/1447/0.018997 | 978/1828/1484/0.017997 | 989/1833/1419/0.016998 |
29 | 9832/15701/15229/1.7937 | 9824/15661/15379/1.8267 | 10778/16930/17516/2.2757 |
30 | 337/676/339/0.005999 | 385/773/390/0.006999 | 395/793/400/0.007998 |
31 | 9/19/10/0.003999 | 7/15/8/0.004999 | 7/15/8/0.004 |
32 | 9/19/10/0.008999 | 7/15/8/0.008999 | 7/15/8/0.006999 |
33 | 9/19/10/0.001 | 8/17/9/0.001 | 8/17/9/0.000999 |
34 | 9/19/10/0.008999 | 8/17/9/0.007999 | 8/17/9/0.007998 |
35 | 10/21/11/0.001 | 9/19/10/0.001 | 9/19/10/0.000999 |
36 | 10/21/11/0.009999 | 9/19/10/0.008998 | 9/19/10/0.008999 |
37 | 12/25/13/0.000999 | 11/23/12/0.001 | 11/23/12/0.001 |
38 | 12/25/13/0.001999 | 11/23/12/0.001999 | 11/23/12/0.001999 |
39 | 48/97/49/0.000999 | 49/99/50/0.001 | 48/97/49/0.000999 |
40 | 167/335/168/0.028996 | 168/337/169/0.024996 | 169/339/170/0.023996 |
41 | 133/267/134/0.019997 | 129/259/130/0.018997 | 127/255/128/0.018997 |
42 | 269/539/270/0.24496 | 265/531/266/0.24396 | 263/527/264/0.25996 |
43 | 54/109/55/0.000999 | 52/105/53/0.001 | 52/105/53/0.000999 |
44 | 83/167/84/0.002999 | 81/163/82/0.003 | 79/159/80/0.002 |
45 | 167/335/168/0.057992 | 169/339/170/0.058991 | 164/329/165/0.054992 |
46 | 263/527/264/0.23896 | 266/533/267/0.24796 | 256/513/257/0.23396 |
47 | 1046/2093/1047/0.030995 | 1057/2115/1058/0.032995 | 938/1877/939/0.027996 |
48 | 2926/5853/2927/0.43093 | 2914/5829/2915/0.43593 | 2918/5837/2919/0.42993 |
49 | 635/1271/636/0.018997 | 607/1215/608/0.018997 | 599/1199/600/0.018997 |
50 | 1467/2935/1468/0.20897 | 1478/2957/1479/0.21497 | 1413/2827/1414/0.21397 |
51 | 606/1213/607/0.019997 | 602/1205/603/0.022997 | 481/963/482/0.013998 |
52 | 1434/2869/1435/0.21897 | 1413/2827/1414/0.20497 | 1387/2775/1388/0.28396 |
53 | 596/1193/597/0.020997 | 604/1209/605/0.018997 | 388/777/389/0.016998 |
54 | 1374/2749/1375/0.20497 | 1424/2849/1425/0.20697 | 1356/2713/1357/0.20697 |
55 | 200/401/202/0.001999 | 200/401/202/0.001999 | 200/401/202/0.001999 |
56 | 1000/2001/1002/0.048992 | 1000/2001/1002/0.06199 | 1000/2001/1002/0.050992 |
57 | 7/15/8/0.002 | 7/15/8/0.002 | 6/13/7/0.001999 |
58 | 7/15/8/0.004 | 7/15/8/0.004999 | 7/15/8/0.003999 |
59 | 28/57/29/0.001 | 27/55/28/0.001 | 27/55/28/0.001 |
60 | 29/59/30/0.000999 | 29/59/30/0.002 | 29/59/30/0.002 |
61 | 32/59/40/0.010999 | 32/60/45/0.009998 | 31/56/39/0.011998 |
62 | 4/9/6/0.001 | 4/9/6/0.001 | 4/9/6/0.001 |
63 | 26/48/33/0.003 | 26/49/33/0.003 | 22/42/28/0.002999 |
64 | 27/50/40/0.016997 | 25/44/34/0.014998 | 23/42/30/0.013998 |
65 | 1151/2285/1599/0.008998 | 1150/2270/1564/0.006998 | 1708/3414/2234/0.013998 |
66 | 5481/11373/6023/0.041993 | 5510/11246/5845/0.041994 | 5906/12296/6550/0.045993 |
67 | 6354/13073/6816/0.47393 | 7741/15623/7929/0.54592 | 7866/16031/8277/0.61791 |
68 | 0/1/1/0.001999 | 0/1/1/0.001999 | 0/1/1/0.001 |
69 | 0/1/1/0.002999 | 0/1/1/0.003 | 0/1/1/0.002 |
70 | F/F/F/F | F/F/F/F | F/F/F/F |
71 | 6604/13682/7147/0.6859 | 4310/8650/4348/0.43493 | 6879/14253/7386/0.74789 |
72 | 368/739/371/0.25896 | 305/611/306/0.20897 | 395/792/397/0.28096 |
73 | 434/869/435/0.54392 | 375/752/377/0.53992 | 460/922/462/0.60891 |
74 | 88/178/90/0.001999 | 92/186/94/0.001999 | 80/162/82/0.002 |
75 | 603/1209/606/0.85987 | 454/910/456/0.6459 | 655/1311/656/0.96185 |
76 | 52/103/80/0.000999 | 107/205/145/0.003 | 36/72/65/0.001 |
77 | 53/107/80/0.047993 | 49/97/74/0.044993 | 33/68/56/0.032995 |
78 | 2720/5482/2769/1.2288 | 1895/4067/2224/0.93486 | 2964/5978/3028/1.3378 |
79 | 6653/13399/6765/14.238 | 5844/12355/6649/12.715 | 7015/14081/7077/14.59 |
80 | 297/631/344/0.005999 | 297/622/337/0.003 | 319/677/367/0.005999 |
81 | 1257/2553/1321/0.070989 | 1094/2231/1154/0.054992 | 1183/2404/1237/0.06899 |
82 | 7/15/10/0.001 | 7/15/10/0 | 7/15/10/0.001 |
83 | 5/11/6/0.001 | 5/11/6/0.001 | 5/11/6/0.001 |
84 | F/F/F/F | F/F/F/F | F/F/F/F |
85 | 18/37/19/0.000999 | 19/40/23/0.001 | 19/39/23/0 |
86 | 23/54/38/0.031995 | 23/50/32/0.028996 | 24/50/30/0.026996 |
87 | 9/19/10/0.013998 | 9/19/10/0.011998 | 10/21/11/0.012998 |
88 | 11/23/12/0.057991 | 10/21/11/0.052991 | 10/21/11/0.052992 |
89 | 334/684/430/0.025996 | 453/910/511/0.027996 | 249/501/306/0.015998 |
90 | 1085/2106/1395/0.75888 | F/F/F/F | 561/1137/584/0.34195 |
91 | 5640/11281/5776/0.024996 | 7051/14103/7209/0.031995 | 4262/8525/4365/0.018997 |
92 | 502/1005/503/0.026996 | 489/979/490/0.020997 | 484/969/485/0.019997 |
93 | 284/577/295/0.012998 | 282/573/293/0.008999 | 282/573/293/0.008998 |
94 | 4753/9513/4762/1.8517 | 5342/10691/5351/1.9547 | 5242/10491/5251/1.9357 |
95 | 356/717/362/0.011998 | 355/716/363/0.017996 | 356/718/364/0.010999 |
96 | 2309/4624/2316/2.6026 | 2209/4425/2218/2.4486 | 2227/4460/2234/2.4826 |
97 | 1801/3346/2059/0.49393 | 1968/3821/2085/0.48993 | 1913/3704/2037/0.47193 |
98 | 9063/17431/9760/22.829 | 8928/17306/9480/22.166 | 8989/17216/9753/23.235 |
99 | 168/329/179/0.005998 | 150/298/154/0.004999 | 160/315/173/0.005999 |
100 | 10/23/16/0.006999 | 10/37/32/0.010998 | 9/31/25/0.008999 |
101 | 8/26/22/0.014997 | 9/22/14/0.011999 | 7/16/10/0.008999 |
102 | 4004/8014/4257/0.11298 | 3540/7087/3693/0.10298 | 1758/3522/1999/0.06199 |
103 | 3027/6061/3162/0.21297 | 2014/4032/2071/0.11298 | 1705/3414/1878/0.10898 |
104 | F/F/F/F | F/F/F/F | F/F/F/F |
105 | 13/26/15/0.001 | 13/28/15/0 | 13/28/15/0 |
106 | 14/28/16/0.001 | 15/31/18/0.002 | 14/29/15/0.001 |
107 | 44/121/84/0.000999 | 47/140/101/0.001 | 41/106/73/0.000999 |
108 | 44/134/98/0.001 | 49/126/87/0.001 | 44/123/87/0.000999 |
109 | 84/141/143/0.009999 | 97/160/158/0.009998 | 81/140/132/0.010999 |
110 | 200/235/367/0.044993 | 211/245/395/0.042994 | 191/224/353/0.038994 |
111 | 70/174/124/0.025997 | 95/214/150/0.024996 | 70/167/118/0.019997 |
112 | F/F/F/F | F/F/F/F | 78/175/124/0.080988 |
113 | 103/214/121/0.001 | 102/206/112/0.000999 | 191/383/237/0.001999 |
114 | 224/461/272/0.11898 | 115/232/124/0.059991 | 201/403/240/0.10798 |
115 | 258/517/259/0.043993 | 762/1525/763/0.13298 | 372/745/373/0.06499 |
116 | 369/739/370/0.12398 | 1116/2233/1117/0.40794 | 473/947/474/0.17397 |
117 | 24/49/25/0.001 | 23/47/24/0.001 | 23/47/24/0.000999 |
118 | 35/71/36/0.016998 | 34/69/35/0.016998 | 34/69/35/0.015997 |
119 | 46/82/58/0.002999 | 44/79/55/0.003 | 44/78/56/0.003 |
120 | 39/65/54/0.26096 | 41/69/56/0.27796 | 41/69/56/0.27096 |
121 | F/F/F/F | F/F/F/F | F/F/F/F |
122 | F/F/F/F | F/F/F/F | F/F/F/F |
123 | F/F/F/F | F/F/F/F | F/F/F/F |
124 | F/F/F/F | F/F/F/F | F/F/F/F |
125 | 24/57/43/0.19897 | 32/72/57/0.25396 | 22/49/32/0.15398 |
126 | 44/108/92/0.010998 | 54/125/104/0.010998 | 43/115/95/0.009999 |
127 | 88/166/179/0.35795 | 68/166/142/0.27996 | 37/95/83/0.16198 |
128 | 164/331/168/0.003 | 185/375/192/0.003 | 165/333/170/0.002999 |
129 | 4499/8999/4500/1.1628 | 5259/10519/5260/1.3568 | 4737/9475/4738/1.2478 |
130 | 21/43/22/0.016998 | 21/43/22/0.016998 | 21/43/22/0.017998 |
131 | 22/45/23/0.039994 | 22/45/23/0.038994 | 22/45/23/0.038994 |
132 | 218/443/227/0.15398 | 206/419/215/0.14698 | 201/409/210/0.14298 |
133 | 225/457/234/0.33295 | 214/435/223/0.33495 | 207/421/216/0.30895 |
134 | 11/24/14/0.001 | 10/22/13/0.001 | 11/24/15/0.001 |
135 | 12/26/16/0.004998 | 10/22/13/0.002999 | 11/24/15/0.003999 |
136 | 12/26/17/0.008999 | 10/22/13/0.006999 | 11/24/15/0.007999 |
137 | 870/1741/871/0.041994 | 856/1713/857/0.033995 | 855/1711/856/0.033995 |
138 | 1641/3283/1642/0.30795 | 1728/3457/1729/0.33695 | 1682/3365/1683/0.32395 |
139 | 122/221/153/0.002999 | 120/221/149/0.001999 | 121/223/150/0.001999 |
140 | 13/26/15/0.000999 | 14/28/16/0.001 | 14/28/16/0.000999 |
141 | 6/13/7/0.003 | 6/13/7/0.003 | 6/13/7/0.002999 |
142 | 156/325/213/0.001 | 130/270/191/0.001 | 137/282/194/0.002 |
143 | 32/61/41/0.001 | 32/60/40/0 | 31/58/37/0.000999 |
144 | 25/62/42/0.002 | 20/76/63/0.002 | 18/45/33/0.002 |
145 | 22/54/39/0.015998 | 18/71/61/0.016997 | 23/72/56/0.014998 |
146 | 92/185/93/0.000999 | 92/185/93/0.001 | 91/183/92/0.000999 |
147 | 338/677/339/0.017997 | 339/679/340/0.016997 | 338/677/339/0.016996 |
148 | 21/43/22/0.001 | 21/43/22/0 | 21/43/22/0 |
149 | 25/51/26/0.001 | 25/51/26/0.001 | 25/51/26/0.001 |
150 | 93/243/150/0.026996 | 101/271/170/0.024996 | 81/214/133/0.019997 |
151 | 119/303/184/0.15498 | 108/291/184/0.14598 | 106/285/184/0.13598 |
152 | 268/554/301/0.082988 | 271/562/303/0.084987 | 157/355/225/0.057991 |
153 | 241/521/308/0.21097 | 208/462/286/0.18797 | 161/358/228/0.17597 |
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