An interior proximal linearized method for DC programming based on Bregman distance or second-order homogeneous kernels. (3rd July 2019)

• Record Type: Journal Article
• Authors: Cruz Neto, J. X.; Lopes, J. O.; Santos, P. S. M.; Souza, J. C. O.
• Is Part Of: Optimization. Volume 68:Number 7(2019)
• Page Start: 1305
• Page End: 1319
• Publication Date: 2019-07-03
• Subjects: Interior proximal methods -- DC functions -- proximal distance -- Bregman distances -- second-order homogeneous kernels; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1476859
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: We present an interior proximal method for solving constrained nonconvex optimization problems where the objective function is given by the difference of two convex function (DC function). To this end, we consider a linearized proximal method with a proximal distance as regularization. Convergence analysis of particular choices of the proximal distance as second-order homogeneous proximal distances and Bregman distances are considered. Finally, some academic numerical results are presented for a constrained DC problem and generalized Fermat–Weber location problems.