Robust SOS-Convex Polynomial Programs: Exact SDP Relaxations

Abstract

This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial programs in the face of data uncertainty. The class of convex programs, called robust SOS-convex programs, includes robust quadratically constrained convex programs and robust separable convex polynomial programs. It establishes sums of squares polynomial representations characterizing robust solutions and exact SDP-relaxations of robust SOS-convex programs under various commonly used uncertainty sets. In particular, the results show that the polytopic and ellipsoidal uncertainty sets, that allow second-order cone re-formulations of robust quadratically constrained programs, continue to permit exact SDP-relaxations for a broad class of robust SOS-convex programs. They also yield exact second-order cone relaxation for robust quadratically constrained programs.

References in corpus (2)

• A convex polynomial that is not sos-convex
• Nonnegative Polynomials and Sums of Squares

Cited by in corpus (6)

• Extending the Scope of Robust Quadratic Optimization
• Piecewise SOS-Convex Moment Optimization and Applications via Exact Semi-Definite Programs
• A Moment-SOS Hierarchy for Robust Polynomial Matrix Inequality Optimization with SOS-Convexity
• Exact Conic Programming Reformulations of Two-Stage Adjustable Robust Linear Programs with New Quadratic Decision Rules
• SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
• Robust Global Solutions of Bilevel Polynomial Optimization Problems with Uncertain Linear Constraints