An aggregate deformation homotopy method for min-max-min problems with max-min constraints

Authors:
Hui-Juan Xiong;Bo Yu
Affiliations:
Department of Mathematics, Dalian University of Technology, Dalian, China;Department of Mathematics, Dalian University of Technology, Dalian, China
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

In this paper, the constrained min-max-min problem, which is an essentially nonsmooth and nonconvex problem, is considered. Based on a twice aggregate function with a modification, an aggregate deformation homotopy method is established. Under some suitable assumptions, a smooth path from a randomly given point to a solution of the generalized KKT system is proven to exist. By numerically tracing the smooth path, a globally convergent algorithm for some solution of the problem is given. Some numerical results are given to show the feasibility of the method.