Separation of Nonconvex Sets with General Augmenting Functions

In this paper, we consider two geometric optimization problems that are dual to each other and characterize conditions under which the optimal values of the two problems are equal. This characterization relies on establishing separation results for nonconvex sets using general concave surfaces defined in terms of convex augmenting functions. We prove separation results for bounded-below augmenting functions, unbounded augmenting functions, and asymptotic augmenting functions. Key words: Augmenting functions, separation of nonconvex sets, asymptotic cone, asymptotic function. MSC2000 subject classification: Primary: 90C30, 90C46. OR/MS subject classification: Primary: Programming/nonlinear.

• Type: Journal
• Year: 2008
• Where: MOR
• Authors: Angelia Nedic, Asuman E. Ozdaglar
• Keywords: Asymptotic Augmenting Functions, Bounded-below Augmenting Functions, MOR 2008, Nonconvex Sets