Superlinearly Convergent Norm-Relaxed SQP Method Based on Active Set Identification and New Line Search for Constrained Minimax Problems

Jin-bao Jian (), Qing-juan Hu () and Chun-ming Tang ()
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Jin-bao Jian: Yulin Normal University
Qing-juan Hu: Luoshan Secondary Vocational School
Chun-ming Tang: Guangxi University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 10, 859-883

Abstract: Abstract In this paper, the minimax problems with inequality constraints are discussed, and an alternative fast convergent method for the discussed problems is proposed. Compared with the previous work, the proposed method has the following main characteristics. First, the active set identification which can reduce the scale and the computational cost is adopted to construct the direction finding subproblems. Second, the master direction and high-order correction direction are computed by solving a new type of norm-relaxed quadratic programming subproblem and a system of linear equations, respectively. Third, the step size is yielded by a new line search which combines the method of strongly sub-feasible direction with the penalty method. Fourth, under mild assumptions without any strict complementarity, both the global convergence and rate of superlinear convergence can be obtained. Finally, some numerical results are reported.

Keywords: Constrained minimax problems; SQP method; Active set identification; Line search; Superlinear convergence (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0503-5

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