Robust generalized S-Procedure

TL;DR

This paper introduces a robust generalized S-procedure for robust optimization, providing primal and dual characterizations and extending it to include a right-hand side function, enhancing its applicability.

Contribution

It presents a new robust S-procedure with primal and dual characterizations and extends it to handle right-hand side functions, advancing robust optimization methods.

Findings

Primal characterization of the robust generalized S-procedure.

Dual characterization under locally convex decision spaces.

Extension incorporating a right-hand side function.

Abstract

We introduce in this paper the so-called robust generalized S-procedure associated with a given robust optimization problem. We provide a primal characterization for the validity of this procedure as well as a dual characterization under the assumption that the decision space is locally convex. We also analyze an extension of the mentioned robust S-procedure that incorporates a right-hand side function.