DC approach to weakly convex optimization and nonconvex quadratic optimization problems

Abstract

Motivated by weakly convex optimization and quadratic optimization problems, we first show that there is no duality gap between a difference of convex (DC) program over DC constraints and its associated dual problem. We then provide certificates of global optimality for a class of nonconvex optimization problems. As an application, we derive characterizations of robust solutions for uncertain general nonconvex quadratic optimization problems over nonconvex quadratic constraints.

Keywords:

• Difference of convex program
• weakly convex
• nonconvex quadratic problem
• convex polynomial
• robust optimization

Notes

No potential conflict of interest was reported by the author.