Robust convex conic optimization in D-induced duality framework

Abstract

Research of convex conic optimization becomes spry thanks to the powerful interior point method while due to uncertainty in practice, robustness of a solution of an optimization problem is emphasized. This article incorporates robustness into a general convex conic optimization problem and shows its deterministic equivalence under the D-duality framework, in which one needs only to compute a D-induced convex cone, which is generally difficult. While for some special case this paper shows that its tractable. Three kinds of applications in robust location, robust fitting and robust multi-stage investment problems are shown to illustrate the unification of this framework

Keywords and phrases:

• Convex conic optimization
• robust optimization
• D-duality, convex cone
• location
• fitting
• multi-stage investment