A Smoothing Method for Sparse Programs by Symmetric Cone Constrained Generalized Equations

Cong Cheng and Lianjie Tang ()
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Cong Cheng: School of Economics and Management, Hebei University of Technology, Tianjin 300401, China
Lianjie Tang: School of Management, Henan University of Technology, Zhengzhou 450001, China

Mathematics, 2023, vol. 11, issue 17, 1-19

Abstract: In this paper, we consider a sparse program with symmetric cone constrained parameterized generalized equations (SPSCC). Such a problem is a symmetric cone analogue with vector optimization, and we aim to provide a smoothing framework for dealing with SPSCC that includes classical complementarity problems with the nonnegative cone, the semidefinite cone and the second-order cone. An effective approximation is given and we focus on solving the perturbation problem. The necessary optimality conditions, which are reformulated as a system of nonsmooth equations, and the second-order sufficient conditions are proposed. Under mild conditions, a smoothing Newton approach is used to solve these nonsmooth equations. Under second-order sufficient conditions, strong BD-regularity at a solution point can be satisfied. An inverse linear program is provided and discussed as an illustrative example, which verified the efficiency of the proposed algorithm.

Keywords: sparse program; symmetric cone constrained; perturbation problem; smoothing Newton method; BD-regularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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