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Hadamard Directional Diff erentiability of the Optimal Value of a Linear Second-order Conic Programming Problem

Duan Qingsong (duanqs***at***dlut.mail.edu.cn)
Zhang Liwei(lwzhang***at***dlut.edu.cn)
Zhang Sainan(sainanzhzh***at***163.com)

Abstract: 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 primal problem and the 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 a Lipschitz continuous function and Hadamard directionally diff erentiable.

Keywords: second order conic optimization, optimal value function, solution mapping, Hadamard directional di fferentiability.

Category 1: Stochastic Programming

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Citation: Manuscrip

Download: [PDF]

Entry Submitted: 03/22/2018
Entry Accepted: 03/25/2018
Entry Last Modified: 03/22/2018

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