On second-order conic programming duals for robust convex quadratic optimization problems

Abstract

In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem with uncertain data in the constraints. We first introduce a SOCP dual problem for this robust convex quadratic optimization problem with polytopic uncertain sets. Then, we obtain a zero duality gap result between this robust convex quadratic optimization problem and its dual problem in terms of a new robust type characteristic cone constraint qualification. We also construct a SOCP dual problem for this robust convex quadratic optimization problem with norm-constrained uncertain sets and obtain the corresponding zero duality gap result between them. Moreover, some numerical examples are given to explain the obtained results.