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Nonmonotone line search algorithm for constrained minimax problems. (English) Zbl 1039.90089
Summary: In this paper, an algorithm for constrained minimax problems is presented which is globally convergent and whose rate of convergence is two-step superlinear. The algorithm applies SQP to the constrained minimax problems by combining a nonmonotone line search and a second-order correction technique, which guarantees a full steplength while close to a solution, such that the Maratos effect is avoided and two-step superlinear convergence is achieved.

MSC:
90C47 Minimax problems in mathematical programming
90C55 Methods of successive quadratic programming type
Software:
FSQP
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References:
[1] MARATOS, N., Exact Penalty Function Algorithms for Finite-Dimensional and Control Optimization Problems, PhD Thesis, Imperial College, University of London, London, England, 1978.
[2] CHAMBERLAIN, R. M., POWELL, M. J. D., LEMARECHAL, C., and PEDERSEN, H. C., The Watchdog Technique for Forcing Convergence in Algorithms for Constrained Optimization, Mathematical Programming Study, Vol. 16, pp. 1–17, 1982. · Zbl 0477.90072 · doi:10.1007/BFb0120945
[3] GRIPPO, L., LAMPARIELLO, F., and LUCIDI, S., A Nonmonotone Line Search Technique for Newton’s Method, SIAM Journal on Numerical Analysis, Vol. 23, pp. 707–716, 1986. · Zbl 0616.65067 · doi:10.1137/0723046
[4] RUSTEM, B., A Constrained Minimax Algorithm for Rival Models of the Same Economic System, Mathematical Programming, Vol. 53, pp. 279–295, 1992. · Zbl 0751.90057 · doi:10.1007/BF01585707
[5] RUSTEM, B., and NGUYEN, Q., An Algorithm for the Inequality-Constrained Discrete Minimax Problem, SIAM Journal on Optimization, Vol. 8, pp. 265–283, 1998. · Zbl 0911.90310 · doi:10.1137/S1056263493260386
[6] LUKSAN, L., and VLCEK, J., Globally Convergent Variable-Metric Method for Convex Nonsmooth Unconstrained Optimization, Journal of Optimization Theory and Applications, Vol. 102, pp. 593–613, 1999. · Zbl 0955.90102 · doi:10.1023/A:1022650107080
[7] ZHOU, J. I., and TITS, A. L., Nonmonotone Line Search for Minimax Problems, Journal of Optimization Theory and Applications, Vol. 76, pp. 455–476, 1991. · Zbl 0792.90079 · doi:10.1007/BF00939377
[8] POWELL, M. J. D., The Convergence of Variable-Metric Methods for Nonlinearly Constrained Optimization Calculations, Nonlinear Programming 3, Edited by O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Academic Press, New York, NY, pp. 27–68, 1978.
[9] POWELL, M. J. D., A Fast Algorithm for Nonlinearly Optimization Calculations, Proceedings of the 1997 Dundee Biennial Conference on Numerical Analysis, Edited by G. A. Watson, Springer Verlag, Berlin, Germany, pp. 144–157, 1978.
[10] HAN, S. P., A Globally Convergent Method for Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 22, pp. 297–309, 1977. · Zbl 0336.90046 · doi:10.1007/BF00932858
[11] PANIER, E. R., and TITS, A. L., Avoiding the Maratos Effect by Means of a Nonmonotone Line Search, Part 1: General Constrained Problems, SIAM Journal on Numerical Analysis, Vol. 28, pp. 1183–1195, 1991. · Zbl 0732.65055 · doi:10.1137/0728063
[12] MAYNE, D. Q., and POLAK, E., A Superlinearly Convergent Algorithm for Constrained Optimization Problems, Mathematical Programming Study, Vol. 16, pp. 45–61, 1982. · Zbl 0477.90071 · doi:10.1007/BFb0120947
[13] YUAN, Y., and SUN, W., Optimization Theory and Methods, Science Press, Beijing, PRC, 1997.
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