Homotopy method for solving mathematical programs with bounded box-constrained variational inequalities. (2nd December 2019)

• Record Type: Journal Article
• Authors: Zhang, Chunyang; Zhu, Zhichuan; Yao, Yonghong; Liu, Qinghuai
• Is Part Of: Optimization. Volume 68:Number 12(2019)
• Page Start: 2297
• Page End: 2316
• Publication Date: 2019-12-02
• Subjects: Equilibrium constraints -- homotopy method -- KKT system -- nonlinear programming; 90C30 -- 65H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1647199
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: On the basis of Robinson's normal equation and smoothing projection operator, a homotopy method for solving mathematical programs with box-constrained variational inequalities (MPBVI) is presented. In which, the Chen–Harker–Kanzow–Smale smooth function is used to transform MPBVI into a smooth optimization problem. Under some mild assumptions, the existence and global convergence of a smooth path from almost any initial point to the GKKT point of the approximate problems is proven. And, the convergence of the GKKT point to a strong C-stationary point of the original problems is proved. Finally, some numerical results are given to show the effectiveness and feasibility of the homotopy method.