|
[1]
|
A. Baums, Minimax method in optimizing energy consumption in real-time embedded systems, Automatic Control and Computer Sciences, 43 (2009), 57-62.
doi: 10.3103/S0146411609020011.
|
|
[2]
|
J. F. Bonnans, J. C. Gilbert, C. Lemaréchal and C. Sagastizábal,
Numerical Optimization: Theoretical and Practical Aspects, Second ed. Springer-Verlag, Berlin Heidelberg New York, 2006.
|
|
[3]
|
J. V. Burke, A. S. Lewis and M. L. Overton, A robust gradient sampling algorithm for nonsmooth, nonconvex optimization, SIAM Journal on Optimization, 15 (2005), 751-779.
doi: 10.1137/030601296.
|
|
[4]
|
F. L. Chernousko, Minimax control for a class of linear systems subject to disturbances, Journal of Optimization Theory and Applications, 127 (2005), 535-548.
doi: 10.1007/s10957-005-7501-1.
|
|
[5]
|
J. Dattorro,
Convex Optimization † Euclidean Distance Geometry, second edn,
$ \mathcal{M}\varepsilonβ oo$, 2015.
|
|
[6]
|
G. Di Pillo, L. Grippo and S. Lucidi, A smooth method for the finite minimax problem, Mathematical Programming, 60 (1993), 187-214.
doi: 10.1007/BF01580609.
|
|
[7]
|
A. Fuduli, M. Gaudioso, G. Giallombardo and G. Miglionico, A partially inexact bundle method for convex semi-infinite minmax problems, Communications in Nonlinear Science and Numerical Simulation, 21 (2015), 172-180.
doi: 10.1016/j.cnsns.2014.07.033.
|
|
[8]
|
M. Gaudioso, G. Giallombardo and G. Miglionico, An incremental method for solving convex finite min-max problems, Mathematics of Operations Research, 31 (2006), 173-187.
doi: 10.1287/moor.1050.0175.
|
|
[9]
|
M. Gaudioso, G. Giallombardo and G. Miglionico, On solving the Lagrangian dual of integer programs via an incremental approach, Computational Optimization and Applications, 44 (2009), 117-138.
doi: 10.1007/s10589-007-9149-2.
|
|
[10]
|
W. Hare and J. Nutini, A derivative-free approximate gradient sampling algorithm for finite minimax problems, Computational Optimization and Applications, 56 (2013), 1-38.
doi: 10.1007/s10589-013-9547-6.
|
|
[11]
|
W. Hare and M. Macklem, Derivative-free optimization methods for finite minimax problems, Optimization Methods and Software, 28 (2013), 300-312.
doi: 10.1080/10556788.2011.638923.
|
|
[12]
|
S. X. He and Y. Y. Nie, A class of nonlinear Lagrangian algorithms for minimax problems, Journal of Industrial and Management Optimization, 9 (2013), 75-97.
doi: 10.3934/jimo.2013.9.75.
|
|
[13]
|
M. Huang, X. J. Liang, Y. Lu and L. P. Pang, The bundle scheme for solving arbitrary eigenvalue optimizations, Journal of Industrial and Management Optimization, 13 (2017), 659-680.
doi: 10.3934/jimo.2016039.
|
|
[14]
|
J. B. Jian, X. L. Zhang, R. Quan and Q. Ma, Generalized monotone line search SQP algorithm for constrained minimax problems, Optimization, 58 (2009), 101-131.
doi: 10.1080/02331930801951140.
|
|
[15]
|
J. B. Jian, X. D. Mo, L. J. Qiu, S. M. Yang and F. S. Wang, Simple sequential quadratically constrained quadratic programming feasible algorithm with active identification sets for constrained minimax problems, Journal of Optimization Theory and Applications, 160 (2014), 158-188.
doi: 10.1007/s10957-013-0339-z.
|
|
[16]
|
J. B. Jian, C. M. Tang and F. Tang, A feasible descent bundle method for inequality constrained minimax problems (in Chinese), Science China: Mathematics, 45 (2015), 2001-2024.
|
|
[17]
|
E. Karas, A. Ribeiro, C. Sagastizábal and M. Solodov, A bundle-filter method for nonsmooth convex constrained optimization, Mathematical Programming, 116 (2009), 297-320.
doi: 10.1007/s10107-007-0123-7.
|
|
[18]
|
N. Karmitsa,
Test Problems for Large-Scale Nonsmooth Minimization, Tech. Rep. No. B. 4/2007, Department of Mathematical Information Technology, University of Jyväskylä, Finland, 2007.
|
|
[19]
|
K. C. Kiwiel, A projection-proximal bundle method for convex nondifferentiable minimization, In: M. Théra, R. Tichatschke (eds.) Ill-posed Variational Problems and Regularization Techniques, Lecture Notes in Econom. Math. Systems, Springer-Verlag, Berlin, 477 (1999), 137–150.
doi: 10.1007/978-3-642-45780-7_9.
|
|
[20]
|
K. C. Kiwiel, A proximal-projection bundle method for Lagrangian relaxation, including semidefinite programming, SIAM Journal on Optimization, 17 (2006), 1015-1034.
doi: 10.1137/050639284.
|
|
[21]
|
K. C. Kiwiel,
Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics, 1133. Springer-Verlag, 1985.
doi: 10.1007/BFb0074500.
|
|
[22]
|
C. Lemaréchal, An extension of Davidon methods to nondifferentiable problems, Mathematical Programming Study, 3 (1975), 95-109.
|
|
[23]
|
X. S. Li and S. C. Fang, On the entropic regularization method for solving min-max problems with applications, Mathematical Methods of Operations Research, 46 (1997), 119-130.
doi: 10.1007/BF01199466.
|
|
[24]
|
Y. P. Li and G. H. Huang, Inexact minimax regret integer programming for long-term planning of municipal solid waste management -- part a: Methodology development, Environmental Engineering Science, 26 (2009), 209-218.
doi: 10.1089/ees.2007.0241.ptA.
|
|
[25]
|
G. Liuzzi, S. Lucidi and M. Sciandrone, A derivative-free algorithm for linearly constrained finite minimax problems, SIAM Journal on Optimization, 16 (2006), 1054-1075.
doi: 10.1137/040615821.
|
|
[26]
|
L. Lukšan and J. Vlček,
Test Problems for Nonsmooth Unconstrained and Linearly Constrained Optimization, Tech. Rep. No. 798, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, 2000.
|
|
[27]
|
K. Madsen and H. Schjær-Jacobsen, Linearly constrained minimax optimization, Mathematical Programming, 14 (1978), 208-223.
doi: 10.1007/BF01588966.
|
|
[28]
|
C. Michelot and F. Plastria, An extended multifacility minimax location problemrevisited, Annals of Operations Research, 111 (2002), 167-179.
doi: 10.1023/A:1020953703533.
|
|
[29]
|
A. Nedić and D. P. Bertsekas, Incremental subgradient methods for nondifferentiable optimization, SIAM Journal on Optimization, 12 (2001), 109-138.
doi: 10.1137/S1052623499362111.
|
|
[30]
|
R. T. Rockafellar,
Convex Analysis, Princeton University Press, Princeton, N. J., 1970.
|
|
[31]
|
B. Rustem and Q. Nguyen, An algorithm for the inequality-constrained discrete min-max problem, SIAM Journal on Optimization, 8 (1998), 265-283.
doi: 10.1137/S1056263493260386.
|
|
[32]
|
C. Sagastizábal and M. Solodov, An infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter, SIAM Journal on Optimization, 16 (2005), 146-169.
doi: 10.1137/040603875.
|
|
[33]
|
N. Z. Shor,
Minimization Methods for Non-differentiable Functions, Springer-Verlag, Berlin, 1985.
doi: 10.1007/978-3-642-82118-9.
|
|
[34]
|
C. M. Tang, H. Y. Chen and J. B. Jian, An improved partial bundle method for linearly constrained minimax problems, Statistics, Optimization and Information Computing, 4 (2016), 84-98.
doi: 10.19139/soic.v4i1.205.
|
|
[35]
|
C. M. Tang and J. B. Jian, Strongly sub-feasible direction method for constrained optimization problems with nonsmooth objective functions, European Journal of Operational Research, 218 (2012), 28-37.
doi: 10.1016/j.ejor.2011.10.055.
|
|
[36]
|
C. M. Tang, S. Liu, J. B. Jian and J. L. Li, A feasible SQP-GS algorithm for nonconvex, nonsmooth constrained optimization, Numerical Algorithms, 65 (2014), 1-22.
doi: 10.1007/s11075-012-9692-5.
|
|
[37]
|
A. Vardi, New minimax algorithm, Journal of Optimization Theory and Applications, 75 (1992), 613-634.
doi: 10.1007/BF00940496.
|
|
[38]
|
F. S. Wang and K. C. Zhang, A hybrid algorithm for nonlinear minimax problems, Annals of Operations Research, 164 (2008), 167-191.
doi: 10.1007/s10479-008-0401-7.
|
|
[39]
|
F. S. Wang and K. C. Zhang, A hybrid algorithm for linearly constrained minimax problems, Annals of Operations Research, 206 (2013), 501-525.
doi: 10.1007/s10479-012-1274-3.
|
|
[40]
|
S. Y. Wang, Y. Yamamoto and M. Yu, A minimax rule for portfolio selection in frictional markets, Mathematical Methods of Operations Research, 57 (2003), 141-155.
doi: 10.1007/s001860200241.
|
|
[41]
|
S. Xu, Smoothing method for minimax problems, Computational Optimization and Applications, 20 (2001), 267-279.
doi: 10.1023/A:1011211101714.
|
|
[42]
|
MOSEK: The MOSEK optimization toolbox for MATLAB manual, Version 7.1 (2016). MOSEK ApS, Denmark, http://www.mosek.com.
|
{{journal.titleEn}} 
DownLoad: 
