Article ID: | iaor2014195 |
Volume: | 160 |
Issue: | 1 |
Start Page Number: | 158 |
End Page Number: | 188 |
Publication Date: | Jan 2014 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Jian Jin-bao, Mo Xing-de, Qiu Li-juan, Yang Su-ming, Wang Fu-sheng |
Keywords: | minimax problem |
In this paper, the nonlinear minimax problems with inequality constraints are discussed. Based on the idea of simple sequential quadratically constrained quadratic programming algorithm for smooth constrained optimization, an alternative algorithm for solving the discussed problems is proposed. Unlike the previous work, at each iteration, a feasible direction of descent called main search direction is obtained by solving only one subprogram which is composed of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the constrained functions. Then a high‐order correction direction used to avoid the Maratos effect is computed by updating the main search direction with a system of linear equations. The proposed algorithm possesses global convergence under weak Mangasarian–Fromovitz constraint qualification and superlinear convergence under suitable conditions with the upper‐level strict complementarity. At last, some preliminary numerical results are reported.