Closedness Type Regularity Conditions in Convex Optimization and Beyond

Frontiers in Applied Mathematics and Statistics

Grad, Sorin-Mihai¹ 

[1] Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany

关键词: convex optimization;    duality;    closedness type regularity conditions;    conjugate functions;    Epigraphs;    Subdifferentials;   

DOI  :  10.3389/fams.2016.00014

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we de- and reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively, for general optimization problems in order to stress that they arise naturally when dealing with such problems. The results are then specialized for constrained and unconstrained convex optimization problems. We also hint towards other classes of optimization problems where closedness type regularity conditions were successfully employed and discuss other possible applications of them.

【 授权许可】

CC BY