Perturbation analysis of a class of conic programming problems under Jacobian uniqueness conditions

Ziran Yin; Liwei Zhang

doi:10.3934/jimo.2018100

Article Contents

2019, Volume 15, Issue 3: 1387-1397. Doi: 10.3934/jimo.2018100

This issue Previous Article Stability in mean for fuzzy differential equation Next Article Necessary optimality conditions for nonautonomous optimal control problems and its applications to bilevel optimal control

Perturbation analysis of a class of conic programming problems under Jacobian uniqueness conditions

Ziran Yin^, and
Liwei Zhang

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

* Corresponding author: Z. R. Yin
* Corresponding author: Z. R. Yin

Received: August 31, 2017

Revised: February 28, 2018

Early access: June 2018

Published: April 2019

The second author is supported by the National Natural Science Foundation of China under projects No. 11571059, No. 11731013 and No. 91330206.

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Abstract

We consider the stability of a class of parameterized conic programming problems which are more general than $C^2$-smooth parameterization. We show that when the Karush-Kuhn-Tucker (KKT) condition, the constraint nondegeneracy condition, the strict complementary condition and the second order sufficient condition (named as Jacobian uniqueness conditions here) are satisfied at a feasible point of the original problem, the Jacobian uniqueness conditions of the perturbed problem also hold at some feasible point.

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Mathematics Subject Classification: 90C31, 49K40, 49J53.

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