Inexact variable metric method for convex-constrained optimization problems. (2nd January 2022)

• Record Type: Journal Article
• Authors: Gonçalves, Douglas S.; Gonçalves, Max L. N.; Menezes, Tiago C.
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 145
• Page End: 163
• Publication Date: 2022-01-02
• Subjects: Convex-constrained optimization problem -- approximate solution -- projected gradient method -- spectral gradient method -- inexact variable metric method; 90Cxx -- 90C30 -- 65Kxx; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1887181
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper is concerned with the inexact variable metric method for solving convex-constrained optimization problems. At each iteration of this method, the search direction is obtained by inexactly minimizing a strictly convex quadratic function over the closed convex feasible set. Here, we propose a new inexactness criterion for the search direction subproblems. Under mild assumptions, we prove that any accumulation point of the sequence generated by the new method is a stationary point of the problem under consideration. In order to illustrate the practical advantages of the new approach, we report some numerical experiments. In particular, we present an application where our concept of the inexact solutions is quite appealing.