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The radius of robust feasibility is the maximal size of uncertain set in which the robust feasible set for an uncertain program is nonempty. In this paper, we employ robust optimization technique to study a class of uncertain convex conic program, and give its formulas for radius of robust feasibility under several data uncertain sets. First, with aid of the distance from the origin to the so-called epigraphcal set, we provide computable upper and lower bounds of the radius of robust feasibility for convex conic program in face of ball uncertainty. Second, a formula is presented for the radius of robust feasibility for robust convex optimization problem with SOS-convex polynomial constraints under ball uncertain sets. Finally, some exact formulas of radius of robust feasibility are given for convex conic program with piecewise linear function constraints under boxes or polytopes uncertain sets.

On Radius of Robust Feasibility for Convex Conic Programs with Data Uncertainty