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On the Levenberg-Marquardt methods for convex constrained nonlinear equations
An outcome space algorithm for minimizing the product of two convex functions over a convex set
1. | School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, N01 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam, Vietnam, Vietnam |
References:
[1] |
H. P. Benson and G. M. Boger, Multiplicative programming problems: Analysis and efficient point search heuristic,, Journal of Optimization Theory and Applications, 94 (1997), 487.
doi: 10.1023/A:1022600232285. |
[2] |
H. P. Benson and G. M. Boger, Outcome-space cutting-plane algorithm for linear multiplicative programming,, Journal of Optimization Theory and Applications, 104 (2000), 301.
doi: 10.1023/A:1004657629105. |
[3] |
H. P. Benson, An outcome space branch and bound-outer approximation algorithm for convex multiplicative programming,, Journal of Global Optimization, 15 (1999), 315.
doi: 10.1023/A:1008316429329. |
[4] |
Y. Gao, G. Wu and W. Ma, A new global optimization approach for convex multiplicative programming,, Applied Mathematics and Computation, 216 (2010), 1206.
doi: 10.1016/j.amc.2010.02.012. |
[5] |
R. Hosrt, N. V. Thoai and J. Devries, On finding the new vertices and redundant constraints in cutting plane algorithms for global optimization,, Operations Research Letters, 7 (1988), 85.
doi: 10.1016/0167-6377(88)90071-5. |
[6] |
B. Jaumard, C. Meyer and H. Tuy, Generalized convex multiplicative programming via quasiconcave minimization,, Journal of Global Optimization, 10 (1997), 229.
doi: 10.1023/A:1008203116882. |
[7] |
N. T. B. Kim, Finite algorithm for minimizing the product of two linear functions over a polyhedron,, Journal Industrial and Management Optimization, 3 (2007), 481.
doi: 10.3934/jimo.2007.3.481. |
[8] |
N. T. B. Kim, N. T. L. Trang and T. T. H. Yen, Outcome-space outer approximation algorithm for linear multiplicative programming,, East West Journal of Mathematics, 9 (2007), 81.
|
[9] |
H. Konno and T. Kuno, Linear multiplicative programming,, Mathematical Programming, 56 (1992), 51.
doi: 10.1007/BF01580893. |
[10] |
H. Konno and T. Kuno, Multiplicative programming problems,, Handbook of Global Optimization, (1995), 369.
|
[11] |
D. T. Luc, "Theory of Vector Optimization,", Springer-Verlag, (1989).
doi: 10.1007/978-3-642-50280-4. |
[12] |
T. Matsui, NP-hardness of linear multiplicative programming and related problems,, Journal of Global Optimization, 9 (1996), 113.
doi: 10.1007/BF00121658. |
[13] |
L. D. Muu and B. T. Tam, Minimizing the sum of a convex function and the product of two affine functions over a convex set,, Optimization, 24 (1992), 57.
doi: 10.1080/02331939208843779. |
[14] |
H. X. Phu, On efficient sets in $\mathbbR^2$,, Vietnam Journal of Mathematics, 33 (2005), 463.
|
[15] |
R. T. Rockafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[16] |
T. V. Thieu, A finite method for globally minimizing concave function over unbounded polyhedral convex sets and its applications,, Acta Mathematica Hungarica, 52 (1988), 21.
doi: 10.1007/BF01952475. |
[17] |
N. V. Thoai, A global optimization approach for solving the convex multiplicative programming problem,, Journal of Global Optimization, 1 (1991), 341.
doi: 10.1007/BF00130830. |
[18] |
P. L. Yu, "Multiple-Criteria Decision Making,", Plenum Press, (1985).
doi: 10.1007/978-1-4684-8395-6. |
show all references
References:
[1] |
H. P. Benson and G. M. Boger, Multiplicative programming problems: Analysis and efficient point search heuristic,, Journal of Optimization Theory and Applications, 94 (1997), 487.
doi: 10.1023/A:1022600232285. |
[2] |
H. P. Benson and G. M. Boger, Outcome-space cutting-plane algorithm for linear multiplicative programming,, Journal of Optimization Theory and Applications, 104 (2000), 301.
doi: 10.1023/A:1004657629105. |
[3] |
H. P. Benson, An outcome space branch and bound-outer approximation algorithm for convex multiplicative programming,, Journal of Global Optimization, 15 (1999), 315.
doi: 10.1023/A:1008316429329. |
[4] |
Y. Gao, G. Wu and W. Ma, A new global optimization approach for convex multiplicative programming,, Applied Mathematics and Computation, 216 (2010), 1206.
doi: 10.1016/j.amc.2010.02.012. |
[5] |
R. Hosrt, N. V. Thoai and J. Devries, On finding the new vertices and redundant constraints in cutting plane algorithms for global optimization,, Operations Research Letters, 7 (1988), 85.
doi: 10.1016/0167-6377(88)90071-5. |
[6] |
B. Jaumard, C. Meyer and H. Tuy, Generalized convex multiplicative programming via quasiconcave minimization,, Journal of Global Optimization, 10 (1997), 229.
doi: 10.1023/A:1008203116882. |
[7] |
N. T. B. Kim, Finite algorithm for minimizing the product of two linear functions over a polyhedron,, Journal Industrial and Management Optimization, 3 (2007), 481.
doi: 10.3934/jimo.2007.3.481. |
[8] |
N. T. B. Kim, N. T. L. Trang and T. T. H. Yen, Outcome-space outer approximation algorithm for linear multiplicative programming,, East West Journal of Mathematics, 9 (2007), 81.
|
[9] |
H. Konno and T. Kuno, Linear multiplicative programming,, Mathematical Programming, 56 (1992), 51.
doi: 10.1007/BF01580893. |
[10] |
H. Konno and T. Kuno, Multiplicative programming problems,, Handbook of Global Optimization, (1995), 369.
|
[11] |
D. T. Luc, "Theory of Vector Optimization,", Springer-Verlag, (1989).
doi: 10.1007/978-3-642-50280-4. |
[12] |
T. Matsui, NP-hardness of linear multiplicative programming and related problems,, Journal of Global Optimization, 9 (1996), 113.
doi: 10.1007/BF00121658. |
[13] |
L. D. Muu and B. T. Tam, Minimizing the sum of a convex function and the product of two affine functions over a convex set,, Optimization, 24 (1992), 57.
doi: 10.1080/02331939208843779. |
[14] |
H. X. Phu, On efficient sets in $\mathbbR^2$,, Vietnam Journal of Mathematics, 33 (2005), 463.
|
[15] |
R. T. Rockafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[16] |
T. V. Thieu, A finite method for globally minimizing concave function over unbounded polyhedral convex sets and its applications,, Acta Mathematica Hungarica, 52 (1988), 21.
doi: 10.1007/BF01952475. |
[17] |
N. V. Thoai, A global optimization approach for solving the convex multiplicative programming problem,, Journal of Global Optimization, 1 (1991), 341.
doi: 10.1007/BF00130830. |
[18] |
P. L. Yu, "Multiple-Criteria Decision Making,", Plenum Press, (1985).
doi: 10.1007/978-1-4684-8395-6. |
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