On the convexification of nonlinear programming problems: An applications-oriented survey

Abstract

Some important classes of decision models give rise to nonconvex minimization problems that, by domain or range transformation, are transformable into convex problems. Thus the powerful theoretical results and the efficiency of algorithms in convex programming can be exploited for a wide range of problems. If no convexifying transformation is at hand, one often requires to approximate a nonconvex objective by a convex one. Then a priori as well as post-computational errorbounds are of interest. The purpose of this paper is to outline briefly some of the ideas and results on convexification that may be useful in practice.