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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Cong Cheng & Lianjie Tang, 2023. "A Smoothing Method for Sparse Programs by Symmetric Cone Constrained Generalized Equations," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3719-:d:1228282
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    References listed on IDEAS

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    1. Yong-Jin Liu & Li-Wei Zhang & Yin-He Wang, 2006. "Some Properties Of A Class Of Merit Functions For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 473-495.
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