HADAMARD DIRECTIONAL DIFFERENTIABILITY OF THE OPTIMAL VALUE OF A LINEAR SECOND-ORDER CONIC PROGRAMMING PROBLEM

摘要

In this paper, we consider perturbation properties of a linear second-order conic optimization problem and its Lagrange dual in which all parameters in the problem are perturbed. We prove the upper semi-continuity of solution mappings for the pertured problem and its Lagrange dual problem. We demonstrate that the optimal value function can be expressed as a min-max optimization problem over two compact convex sets, and it is proven as a Lipschitz continuous function and Hadamard directionally differentiable.