On Approximate Solutions for Robust Convex Optimization Problems (Nonlinear Analysis and Convex Analysis)

Abstract

We review our results for approximate solutions for a robust convex optimization problem with a geometric constraint, which is the face of data uncertainty. In this review, we notice that using robust optimization approach(worst-case approach), we can get an optimality theorem and duality theorems for approximate solutions for the robust convex optimization problem, and that we can extend the optimality and duality results for the convex optimization problem to a fractional optimization problem with uncertainty data.