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An improved SQP algorithm for solving minimax problems. (English) Zbl 1189.90193

Summary: An improved SQP method is proposed for solving minimax problems, and a new method with small computational cost is proposed to avoid the Maratos effect. In addition, its global and superlinear convergence are obtained under some suitable conditions.

MSC:

90C47 Minimax problems in mathematical programming
90C55 Methods of successive quadratic programming type
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References:

[1] Han, S. P., Variable metric methods for minimizing a class of nondifferentiable functions, Math. Program., 20, 1-13 (1981) · Zbl 0441.90095
[2] Polak, E.; Mayne, D. Q.; Higgins, J. E., Superlinearly convergent algorithm for Min-Max problems, J. Optim. Theory Appl., 69, 407-439 (1991) · Zbl 0724.90066
[3] Vardi, A., New Minimax algorithm, J. Optim. Theory Appl., 75, 613-634 (1992) · Zbl 0792.90076
[4] Zhou, J. L.; Tits, A. L., Nonmonotone line search for Minimax problems, J. Optim. Theory Appl., 76, 455-476 (1993) · Zbl 0792.90079
[5] Zhu, Z. B.; Zhang, K. C., A superlinearly convergent sequential quadratic programming algorithm for minimax problems, J. Numer. Math. Appl., 27, 4, 15-32 (2005) · Zbl 1119.90074
[6] Husain, I.; Jabeen, Z., Continuous-time fractional minmax programming, Math. Comput. Modelling, 42, 701-710 (2005) · Zbl 1089.90058
[7] Facchinei, F.; Lucidi, S., Quadratically and superlinearly convergent for the solution of inequality constrained optimization problem, J. Optim. Theory Appl., 85, 2, 265-289 (1995) · Zbl 0830.90125
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