[1]
|
E. G. Birgin, J. M. Martínez and M. Raydan, Algorithm 813: SPG—software for convex-constrained optimization, ACM Trans. Math. Softw., 27 (2001), 340-349.
|
[2]
|
G. R. Bitran and A. C. Hax, Disaggregation and resource allocation using convex knapsack problems with bounded variables, Manag. Sci., 27 (1981), 431-441.
doi: 10.1287/mnsc.27.4.431.
|
[3]
|
B. E. Boser, I. M. Guyon and V. N. Vapnik, A training algorithm for optimal margin classifiers, in Proc. 5th Annu. Wkshp. Comput. Learning Theory (COLT'92) (ed. D. Haussler), ACM Press, (1992), 144–152.
|
[4]
|
K. M. Bretthauer and B. Shetty, Quadratic resource allocation with generalized upper bounds, Oper. Res. Lett., 20 (1997), 51-57.
doi: 10.1016/S0167-6377(96)00039-9.
|
[5]
|
K. M. Bretthauer, B. Shetty and S. Syam, A branch-and-bound algorithm for integer quadratic knapsack problems, ORSA J. Comput., 7 (1995), 109-116.
doi: 10.1287/ijoc.7.1.109.
|
[6]
|
K. M. Bretthauer, B. Shetty and S. Syam, A projection method for the integer quadratic knapsack problem, J. Oper. Res. Soc., 47 (1996), 457-462.
doi: 10.1057/jors.1996.44.
|
[7]
|
P. Brucker, An O($n$) algorithm for quadratic knapsack problems, Oper. Res. Lett., 3 (1984), 163-166.
doi: 10.1016/0167-6377(84)90010-5.
|
[8]
|
P. H. Calamai and J. J. Moré, Quasi-Newton updates with bounds, SIAM J. Numer. Anal., 24 (1987), 1434-1441.
doi: 10.1137/0724092.
|
[9]
|
R. Cominetti, W. F. Mascarenhas and P. J. S. Silva, A Newton's method for the continuous quadratic knapsack problem, Math. Prog. Comp., 6 (2014), 151-169.
doi: 10.1007/s12532-014-0066-y.
|
[10]
|
C. Cortes and V. Vapnik, Support-vector networks, Machine Learning, 20 (1995), 273-297.
|
[11]
|
S. Cosares and D. S. Hochbaum, Strongly polynomial algorithms for the quadratic transportation problem with a fixed number of sources, Math. Oper. Res., 19 (1994), 94-111.
doi: 10.1287/moor.19.1.94.
|
[12]
|
R. W. Cottle, S. G. Duvall and K. Zikan, A Lagrangian relaxation algorithm for the constrained matrix problem, Nav. Res. Logist. Q., 33 (1986), 55-76.
doi: 10.1002/nav.3800330106.
|
[13]
|
Y.-H. Dai and R. Fletcher, New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds, Math. Program., 106 (2006), 403-421.
doi: 10.1007/s10107-005-0595-2.
|
[14]
|
T. A. Davis, W. W. Hager and J. T. Hungerford, An efficient hybrid algorithm for the separable convex quadratic knapsack problem, ACM Trans. Math. Softw., 42 Article 22 (2016), 25 pages.
doi: 10.1145/2828635.
|
[15]
|
J.-P. Dussault, J. A. Ferland and B. Lemaire, Convex quadratic programming with one constraint and bounded variables, Math. Program., 36 (1986), 90-104.
doi: 10.1007/BF02591992.
|
[16]
|
B. C. Eaves, On quadratic programming, Manag. Sci., 17 (1971), 698-711.
doi: 10.1287/mnsc.17.11.698.
|
[17]
|
C. Edirisinghe and J. Jeong, Tight bounds on indefinite separable singly-constrained quadratic programs in linear-time, Math. Program., 164 (2017), 193-227.
doi: 10.1007/s10107-016-1082-7.
|
[18]
|
A. Frangioni and E. Gorgone, A library for continuous convex separable quadratic knapsack problems, Eur. J. Oper. Res., 229 (2013), 37-40.
doi: 10.1016/j.ejor.2013.02.038.
|
[19]
|
W. W. Hager and J. T. Hungerford, Continuous quadratic programming formulations of optimization problems on graphs, Eur. J. Oper. Res., 240 (2015), 328-337.
doi: 10.1016/j.ejor.2014.05.042.
|
[20]
|
W. W. Hager and Y. Krylyuk, Graph partitioning and continuous quadratic programming, SIAM J. Disc. Math., 12 (1999), 500-523.
doi: 10.1137/S0895480199335829.
|
[21]
|
M. Held, P. Wolfe and H. P. Crowder, Validation of subgradient optimization, Math. Program., 6 (1974), 62-88.
doi: 10.1007/BF01580223.
|
[22]
|
R. Helgason, J. Kennington and H. Lall, A polynomially bounded algorithm for a singly constrained quadratic program, Math. Program., 18 (1980), 338-343.
doi: 10.1007/BF01588328.
|
[23]
|
D. S. Hochbaum and S. P. Hong, About strongly polynomial time algorithms for quadratic optimization over submodular constraints, Math. Program., 69 (1995), 269-309.
doi: 10.1007/BF01585561.
|
[24]
|
J. Jeong, Indefinite Knapsack Separable Quadratic Programming: Methods and Applications, Ph.D. Dissertation, University of Tennessee, Knoxville, 2014. Available from: https://trace.tennessee.edu/utk_graddiss/2704/
|
[25]
|
N. Katoh, A. Shioura and T. Ibaraki, Resource allocation problems, in Handbook of Combinatorial Optimization (eds. P.M. Pardalos, DZ Du and R.L. Graham), Springer, (2013), 2897–2988.
doi: 10.1007/978-1-4419-7997-1.
|
[26]
|
K. C. Kiwiel, On linear-time algorithms for the continuous quadratic knapsack problem, J. Optim. Theory Appl., 134 (2007), 549-554.
doi: 10.1007/s10957-007-9259-0.
|
[27]
|
K. C. Kiwiel, Breakpoint searching algorithms for the continuous quadratic knapsack problem, Math. Program., 112 (2008), 473-491.
doi: 10.1007/s10107-006-0050-z.
|
[28]
|
K. C. Kiwiel, Variable fixing algorithms for the continuous quadratic knapsack problem, J. Optim. Theory Appl., 136 (2008), 445-458.
doi: 10.1007/s10957-007-9317-7.
|
[29]
|
N. Maculan, C. P. Santiago, E. M. Macambira and M. H. C. Jardim, An $O(n)$ algorithm for projecting a vector on the intersection of a hyperplane and a box in $\mathbb{R}^n$, J. Optim. Theory Appl., 117 (2003), 553-574.
doi: 10.1023/A:1023997605430.
|
[30]
|
N. Megiddo and A. Tamir, Linear time algorithms for some separable quadratic programming problems, Oper. Res. Lett., 13 (1993), 203-211.
doi: 10.1016/0167-6377(93)90041-E.
|
[31]
|
S. S. Nielsen and S. A. Zenios, Massively parallel algorithms for singly constrained convex programs, ORSA J. Comput., 4 (1992), 166-181.
doi: 10.1287/ijoc.4.2.166.
|
[32]
|
P. M. Pardalos and N. Kovoor, An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds, Math. Program., 46 (1990), 321-328.
doi: 10.1007/BF01585748.
|
[33]
|
P. M. Pardalos, Y. Ye and C.-G. Han, Algorithms for the solution of quadratic knapsack problems, Linear Algebra Appl., 152 (1991), 69-91.
doi: 10.1016/0024-3795(91)90267-Z.
|
[34]
|
M. Patriksson, A survey on the continuous nonlinear resource allocation problem, Eur. J. Oper. Res., 185 (2008), 1-46.
doi: 10.1016/j.ejor.2006.12.006.
|
[35]
|
M. Patriksson and C. Strömberg, Algorithms for the continuous nonlinear resource allocation problem–-New implementations and numerical studies, Eur. J. Oper. Res., 243 (2015), 703-722.
doi: 10.1016/j.ejor.2015.01.029.
|
[36]
|
A. G. Robinson, N. Jiang and C. S. Lerme, On the continuous quadratic knapsack problem, Math. Program., 55 (1992), 99-108.
doi: 10.1007/BF01581193.
|
[37]
|
B. Shetty and R. Muthukrishnan, A parallel projection for the multicommodity network model, J. Oper. Res. Soc., 41 (1990), 837-842.
|
[38]
|
H.-M. Sun and R.-L. Sheu, Minimum variance allocation among constrained intervals, J. Glob. Optim., 74 (2019), 21-44.
doi: 10.1007/s10898-019-00748-3.
|
[39]
|
J. A. Ventura, Computational development of a Lagrangian dual approach for quadratic networks, Networks, 21 (1991), 469-485.
doi: 10.1002/net.3230210407.
|