Indexed by:期刊论文
Date of Publication:2014-01-01
Journal:JOURNAL OF GLOBAL OPTIMIZATION
Included Journals:SCIE、EI
Volume:58
Issue:1
Page Number:151-168
ISSN No.:0925-5001
Key Words:Variational inequality problems; Homotopy method; Smoothing projection operator; Global convergence
Abstract:In this paper, based on the Robinson's normal equation and the smoothing projection operator, a smoothing homotopy method is presented for solving variational inequality problems on polyhedral convex sets. We construct a new smoothing projection operator onto the polyhedral convex set, which is feasible, twice continuously differentiable, uniformly approximate to the projection operator, and satisfies a special approximation property. It is computed by solving nonlinear equations in a neighborhood of the nonsmooth points of the projection operator, and solving linear equations with only finite coefficient matrices for other points, which makes it very efficient. Under the assumption that the variational inequality problem has no solution at infinity, which is a weaker condition than several well-known ones, the existence and global convergence of a smooth homotopy path from almost any starting point in R-n are proven. The global convergence condition of the proposed homotopy method is same with that of the homotopy method based on the equivalent KKT system, but the starting point of the proposed homotopy method is not necessarily an interior point, and the efficiency is more higher. Preliminary test results show that the proposed method is practicable, effective and robust.
Professor
Supervisor of Doctorate Candidates
Supervisor of Master's Candidates
Gender:Male
Alma Mater:吉林大学
Degree:Doctoral Degree
School/Department:数学科学学院
Discipline:Computational Mathematics. Financial Mathematics and Actuarial Science
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