Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems

Jin-bao Jian (), Xing- de Mo (), Li-juan Qiu (), Su-ming Yang () and Fu-sheng Wang ()
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Jin-bao Jian: Yulin Normal University
Xing- de Mo: Guangxi University
Li-juan Qiu: Guangxi University
Su-ming Yang: Guangxi Technological College of Machinery and Electricity
Fu-sheng Wang: Taiyan Normal University

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 1, No 8, 158-188

Abstract: Abstract 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.

Keywords: Inequality constraints; Minimax problems; Simple quadratically constrained quadratic programming; Feasible algorithm; Global and superlinear convergence (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-013-0339-z

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