Convergence analysis of a proximal point algorithm for minimizing differences of functions. (2nd January 2017)

• Record Type: Journal Article
• Authors: An, Nguyen Thai; Nam, Nguyen Mau
• Is Part Of: Optimization. Volume 66:Number 1(2017)
• Page Start: 129
• Page End: 147
• Publication Date: 2017-01-02
• Subjects: DC programming -- proximal point algorithm -- difference of convex functions -- Kurdyka–ᴌojasiewicz inequality; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1253694
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A significant progress to go beyond convexity was made by considering the class of functions representable as differences of convex functions. In this paper, we introduce a generalized proximal point algorithm to minimize the difference of a nonconvex function and a convex function. We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka–ᴌojasiewicz property.