-
Previous Article
Solution properties and error bounds for semi-infinite complementarity problems
- JIMO Home
- This Issue
-
Next Article
Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces
A class of nonlinear Lagrangian algorithms for minimax problems
1. | School of Science, Wuhan University of Technology, Wuhan Hubei, 430070, China, China |
References:
[1] |
A. Ben-Tal and A. Nemirovski, "Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications," MPS/SIAM Ser. Optim. 2, SIAM, Philadelphia, 2001. |
[2] |
D. P. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods," Academic Press, New York, 1982. |
[3] |
C. Charalambous, Acceleration of the least $p$th algorithm for minimax optimization with engineering applications, Math. Program., 19 (1979), 270-297. |
[4] |
G. Dipillo, L. Grippo and S. Lucidi, A smooth method for the finite minimax problem, Math. Program., 60 (1993), 187-214. |
[5] |
J. P. Dussault, Augmented non-quadratic penalty algorithms, Math. Program., 99 (2004), 467-486. |
[6] |
G. D. Erdmann, "A New Minimax Algorithm and Its Application to Optics Problems," Ph. D. Thesis, University of Minnesota, USA, 2003. |
[7] |
S. X. He and L. W. Zhang, Convergence of a dual algorithm for minimax problems, Arch. Control Sci., 10 (2000), 47-60. |
[8] |
Q. J. Hu, Y. Chen, N. P. Chen and X. Q. Li, A modified SQP algorithm for minimax problems, J. Math. Anal. Appl., 360 (2009), 211-222. |
[9] |
J. B. Jian, R. Quan and X. L. Zhang, Generalized monotone line search algorithm for degenerate nonlinear minimax problems, Bull. Austral. Math. Soc., 73 (2006), 117-127.
doi: 10.1017/S0004972700038673. |
[10] |
J. B. Jian, R. Quan and X. L. Zhang, Feasible generalized monotone line search SQP algorithm for nonlinear minimax problems with inequality constraints, J. Comput. Appl. Math., 205 (2007), 406-429. |
[11] |
X. S. Li, An entropy-based aggregate method for minimax optimization, Eng. Optim., 18 (1992), 277-285. |
[12] |
L. Lukšan, C. Matonoha and J. Vlček, Primal interior-point method for large sparse minimax optimization, Tech. Rep. V-941, ICS AS CR, 2005. |
[13] |
E. Y. Pee and J. O. Royset, On solving large-scale finite minimax problems using exponential smoothing, J. Optimiz. Theory App., 148 (2011), 390-1021.
doi: 10.1007/s10957-010-9759-1. |
[14] |
E. Polak, On the mathematical foundations of nondifferentiable optimization in engineering design, SIAM Rev., 29 (1987), 21-89.
doi: 10.1137/1029002. |
[15] |
E. Polak, S. Salcudean and D. Q. Mayne, Adaptive control of ARMA plants using worst-case design by semi-infinite optimization, IEEE Trans. Autom. Control, 32 (1987), 388-397. |
[16] |
E. Polak, "Optimization: Algorithms and Consistent Approximations," Springer-Verlag, New York, NY, 1997. |
[17] |
E. Polak, J. E. Higgins and D. Q. Mayne, A barrier function method for minimax problems, Math. Program., 54 (1992), 155-176. |
[18] |
E. Polak, J. O. Royset and R. S. Womersley, Algorithms with adaptive smoothing for finite minimax problems, J. Optimiz. Theory App., 119 (2003), 459-484.
doi: 10.1023/B:JOTA.0000006685.60019.3e. |
[19] |
R. A. Polyak, Smooth optimization methods for minimax problems, SIAM J. Control Optim., 26 (1988), 1274-1286. |
[20] |
R. A. Polyak, Nonlinear rescaling in discrete minimax, in "Nonsmooth/Nonconvex Mechanics: Modeling, Analysis, Numerical Methods" (eds. R. Ogden and G. Stavroulakis), Kluwer Academic Publishers, Norwell, (2000) (with L. Griva, J. Sobieski). |
[21] |
R. A. Polyak, Modified barrier function: Theory and mehtods, Math. Program., 54 (1992), 177-222. |
[22] |
R. A. Polyak, Log-Sigmoid multipliers method in constrained optimization, Ann. Oper. Res., 101 (2001), 427-460. |
[23] |
R. A. Polyak, Nonlinear rescaling vs. smoothing technique in convex optimization, Math. Program., 92 (2002), 197-235. |
[24] |
S. Xu, Smoothing method for minimax problems, Comput. Optim. Appl., 20 (2001), 267-279. |
[25] |
S. E. Sussman-Fort, Approximate direct-search minimax circuit optimization, Int. J. Numer. Methods Eng., 28 (1989), 359-368. |
[26] |
F. S. Wang and Y. P. Wang, Nonmontone algorithm for minimax optimization problems, Appl. Math. Comput., 217 (2011), 6296-6308. |
[27] |
A. D. Warren, L. S. Lasdon and D. F. Suchman, Optimization in engineering design, Proc. IEEE, 55 (1967), 1885-1897. |
[28] |
F. Ye, H. W. Liu, S. S. Zhou and S. Y. Liu, A smoothing trust-region Newton-CG method for minimax problem, Appl. Math. Comput., 199 (2008), 581-589.
doi: 10.1016/j.amc.2007.10.070. |
[29] |
L. W. Zhang, Y. H. Ren, Y. Wu and X. T. Xiao, A class of nonlinear Lagrangians: Theory and algorithm, Asia-Pac. J. Oper. Res., 25 (2008), 327-371.
doi: 10.1142/S021759590800178X. |
[30] |
L. W. Zhang and H. W. Tang, A maximum entropy algorithm with parameters for solving minimax problem, Arch. Control Sci., 6 (1997), 47-59. |
show all references
References:
[1] |
A. Ben-Tal and A. Nemirovski, "Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications," MPS/SIAM Ser. Optim. 2, SIAM, Philadelphia, 2001. |
[2] |
D. P. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods," Academic Press, New York, 1982. |
[3] |
C. Charalambous, Acceleration of the least $p$th algorithm for minimax optimization with engineering applications, Math. Program., 19 (1979), 270-297. |
[4] |
G. Dipillo, L. Grippo and S. Lucidi, A smooth method for the finite minimax problem, Math. Program., 60 (1993), 187-214. |
[5] |
J. P. Dussault, Augmented non-quadratic penalty algorithms, Math. Program., 99 (2004), 467-486. |
[6] |
G. D. Erdmann, "A New Minimax Algorithm and Its Application to Optics Problems," Ph. D. Thesis, University of Minnesota, USA, 2003. |
[7] |
S. X. He and L. W. Zhang, Convergence of a dual algorithm for minimax problems, Arch. Control Sci., 10 (2000), 47-60. |
[8] |
Q. J. Hu, Y. Chen, N. P. Chen and X. Q. Li, A modified SQP algorithm for minimax problems, J. Math. Anal. Appl., 360 (2009), 211-222. |
[9] |
J. B. Jian, R. Quan and X. L. Zhang, Generalized monotone line search algorithm for degenerate nonlinear minimax problems, Bull. Austral. Math. Soc., 73 (2006), 117-127.
doi: 10.1017/S0004972700038673. |
[10] |
J. B. Jian, R. Quan and X. L. Zhang, Feasible generalized monotone line search SQP algorithm for nonlinear minimax problems with inequality constraints, J. Comput. Appl. Math., 205 (2007), 406-429. |
[11] |
X. S. Li, An entropy-based aggregate method for minimax optimization, Eng. Optim., 18 (1992), 277-285. |
[12] |
L. Lukšan, C. Matonoha and J. Vlček, Primal interior-point method for large sparse minimax optimization, Tech. Rep. V-941, ICS AS CR, 2005. |
[13] |
E. Y. Pee and J. O. Royset, On solving large-scale finite minimax problems using exponential smoothing, J. Optimiz. Theory App., 148 (2011), 390-1021.
doi: 10.1007/s10957-010-9759-1. |
[14] |
E. Polak, On the mathematical foundations of nondifferentiable optimization in engineering design, SIAM Rev., 29 (1987), 21-89.
doi: 10.1137/1029002. |
[15] |
E. Polak, S. Salcudean and D. Q. Mayne, Adaptive control of ARMA plants using worst-case design by semi-infinite optimization, IEEE Trans. Autom. Control, 32 (1987), 388-397. |
[16] |
E. Polak, "Optimization: Algorithms and Consistent Approximations," Springer-Verlag, New York, NY, 1997. |
[17] |
E. Polak, J. E. Higgins and D. Q. Mayne, A barrier function method for minimax problems, Math. Program., 54 (1992), 155-176. |
[18] |
E. Polak, J. O. Royset and R. S. Womersley, Algorithms with adaptive smoothing for finite minimax problems, J. Optimiz. Theory App., 119 (2003), 459-484.
doi: 10.1023/B:JOTA.0000006685.60019.3e. |
[19] |
R. A. Polyak, Smooth optimization methods for minimax problems, SIAM J. Control Optim., 26 (1988), 1274-1286. |
[20] |
R. A. Polyak, Nonlinear rescaling in discrete minimax, in "Nonsmooth/Nonconvex Mechanics: Modeling, Analysis, Numerical Methods" (eds. R. Ogden and G. Stavroulakis), Kluwer Academic Publishers, Norwell, (2000) (with L. Griva, J. Sobieski). |
[21] |
R. A. Polyak, Modified barrier function: Theory and mehtods, Math. Program., 54 (1992), 177-222. |
[22] |
R. A. Polyak, Log-Sigmoid multipliers method in constrained optimization, Ann. Oper. Res., 101 (2001), 427-460. |
[23] |
R. A. Polyak, Nonlinear rescaling vs. smoothing technique in convex optimization, Math. Program., 92 (2002), 197-235. |
[24] |
S. Xu, Smoothing method for minimax problems, Comput. Optim. Appl., 20 (2001), 267-279. |
[25] |
S. E. Sussman-Fort, Approximate direct-search minimax circuit optimization, Int. J. Numer. Methods Eng., 28 (1989), 359-368. |
[26] |
F. S. Wang and Y. P. Wang, Nonmontone algorithm for minimax optimization problems, Appl. Math. Comput., 217 (2011), 6296-6308. |
[27] |
A. D. Warren, L. S. Lasdon and D. F. Suchman, Optimization in engineering design, Proc. IEEE, 55 (1967), 1885-1897. |
[28] |
F. Ye, H. W. Liu, S. S. Zhou and S. Y. Liu, A smoothing trust-region Newton-CG method for minimax problem, Appl. Math. Comput., 199 (2008), 581-589.
doi: 10.1016/j.amc.2007.10.070. |
[29] |
L. W. Zhang, Y. H. Ren, Y. Wu and X. T. Xiao, A class of nonlinear Lagrangians: Theory and algorithm, Asia-Pac. J. Oper. Res., 25 (2008), 327-371.
doi: 10.1142/S021759590800178X. |
[30] |
L. W. Zhang and H. W. Tang, A maximum entropy algorithm with parameters for solving minimax problem, Arch. Control Sci., 6 (1997), 47-59. |
[1] |
Hssaine Boualam, Ahmed Roubi. Augmented Lagrangian dual for nonconvex minimax fractional programs and proximal bundle algorithms for its resolution. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022100 |
[2] |
Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557 |
[3] |
Hssaine Boualam, Ahmed Roubi. Dual algorithms based on the proximal bundle method for solving convex minimax fractional programs. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1897-1920. doi: 10.3934/jimo.2018128 |
[4] |
Brahim El Asri. The value of a minimax problem involving impulse control. Journal of Dynamics and Games, 2019, 6 (1) : 1-17. doi: 10.3934/jdg.2019001 |
[5] |
Xiayang Zhang, Yuqian Kong, Shanshan Liu, Yuan Shen. A relaxed parameter condition for the primal-dual hybrid gradient method for saddle-point problem. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022008 |
[6] |
Yang Li, Yonghong Ren, Yun Wang, Jian Gu. Convergence analysis of a nonlinear Lagrangian method for nonconvex semidefinite programming with subproblem inexactly solved. Journal of Industrial and Management Optimization, 2015, 11 (1) : 65-81. doi: 10.3934/jimo.2015.11.65 |
[7] |
Gabriella Pinzari. Global Kolmogorov tori in the planetary $\boldsymbol N$-body problem. Announcement of result. Electronic Research Announcements, 2015, 22: 55-75. doi: 10.3934/era.2015.22.55 |
[8] |
Yazheng Dang, Jie Sun, Honglei Xu. Inertial accelerated algorithms for solving a split feasibility problem. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1383-1394. doi: 10.3934/jimo.2016078 |
[9] |
Luis Bayón, Jose Maria Grau, Maria del Mar Ruiz, Pedro Maria Suárez. A hydrothermal problem with non-smooth Lagrangian. Journal of Industrial and Management Optimization, 2014, 10 (3) : 761-776. doi: 10.3934/jimo.2014.10.761 |
[10] |
Simon Hubmer, Andreas Neubauer, Ronny Ramlau, Henning U. Voss. On the parameter estimation problem of magnetic resonance advection imaging. Inverse Problems and Imaging, 2018, 12 (1) : 175-204. doi: 10.3934/ipi.2018007 |
[11] |
Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial and Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485 |
[12] |
David Bourne, Howard Elman, John E. Osborn. A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part II: Analysis of Convergence. Communications on Pure and Applied Analysis, 2009, 8 (1) : 143-160. doi: 10.3934/cpaa.2009.8.143 |
[13] |
Siqi Li, Weiyi Qian. Analysis of complexity of primal-dual interior-point algorithms based on a new kernel function for linear optimization. Numerical Algebra, Control and Optimization, 2015, 5 (1) : 37-46. doi: 10.3934/naco.2015.5.37 |
[14] |
Antonio Giorgilli, Stefano Marmi. Convergence radius in the Poincaré-Siegel problem. Discrete and Continuous Dynamical Systems - S, 2010, 3 (4) : 601-621. doi: 10.3934/dcdss.2010.3.601 |
[15] |
S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial and Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155 |
[16] |
Andaluzia Matei, Mircea Sofonea. Dual formulation of a viscoplastic contact problem with unilateral constraint. Discrete and Continuous Dynamical Systems - S, 2013, 6 (6) : 1587-1598. doi: 10.3934/dcdss.2013.6.1587 |
[17] |
Thi Tuyet Trang Chau, Pierre Ailliot, Valérie Monbet, Pierre Tandeo. Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022054 |
[18] |
Saeid Abbasi-Parizi, Majid Aminnayeri, Mahdi Bashiri. Robust solution for a minimax regret hub location problem in a fuzzy-stochastic environment. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1271-1295. doi: 10.3934/jimo.2018083 |
[19] |
Hua-Ping Wu, Min Huang, W. H. Ip, Qun-Lin Fan. Algorithms for single-machine scheduling problem with deterioration depending on a novel model. Journal of Industrial and Management Optimization, 2017, 13 (2) : 681-695. doi: 10.3934/jimo.2016040 |
[20] |
Yifan Xu. Algorithms by layer-decomposition for the subgraph recognition problem with attributes. Journal of Industrial and Management Optimization, 2005, 1 (3) : 337-343. doi: 10.3934/jimo.2005.1.337 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]