A superlinear space decomposition algorithm for constrained nonsmooth convex program

Authors:
Yuan Lu;Li-Ping Pang;Fang-Fang Guo;Zun-Quan Xia
Affiliations:
School of Sciences, Shenyang University, Shenyang 110044, China;School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

A class of constrained nonsmooth convex optimization problems, that is, piecewise C^2 convex objectives with smooth convex inequality constraints are transformed into unconstrained nonsmooth convex programs with the help of exact penalty function. The objective functions of these unconstrained programs are particular cases of functions with primal-dual gradient structure which has connection with VU space decomposition. Then a VU space decomposition method for solving this unconstrained program is presented. This method is proved to converge with local superlinear rate under certain assumptions. An illustrative example is given to show how this method works.