区间值优化问题的 KKT 和弱互补近似 KKT 条件

Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (6): 1897-1913.

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KKT and Weakly Complementary Approximate KKT Conditions for Interval-Valued Optimization Problems

Huang Xiaomei¹(),Tang Guoji^1,^2,^*()

¹School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006
²School of Mathematics and Physics & Center for Applied Mathematics of Guangxi & Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006

Received:2022-12-23 Revised:2023-03-23 Online:2023-12-26 Published:2023-11-16
Supported by:
NSFC(11961006);NSF of Guangxi Province(2020GXNSFAA159100)

Abstract

Abstract:

In this paper, the Karush-Kuhn-Tucker (KKT) and the weakly complementary approximate Karush-Kuhn-Tucker (W-CAKKT) optimality conditions for an LU-solution of the interval-valued optimization problem with inequality and equality constraints (IVOP) are investigated, where the interval-valued objective function is weakly continuously differentiable. Firstly, under suitable constraint qualification, it is proved that the KKT condition is necessary for an LU-solution of (IVOP). Secondly, the W-CAKKT condition is introduced. Absence of any constraint qualification, it is proved that the W-CAKKT condition is necessary for an LU-solution of (IVOP). In addition, under the assumption of convexity, the W-CAKKT condition is sufficient for an LU-solution of (IVOP). Moreover, when some constraint qualification is satisfied, it is shown that the W-CAKKT necessary condition is better than the KKT necessary condition. The results presented in this paper generalize known results from scalar optimization problems to interval-valued optimization problems.

Key words: Interval-Valued optimization problem, Complementary approximate KKT condition, LU-solution, Constraint qualification

CLC Number:

O221

Huang Xiaomei, Tang Guoji. KKT and Weakly Complementary Approximate KKT Conditions for Interval-Valued Optimization Problems[J].Acta mathematica scientia,Series A, 2023, 43(6): 1897-1913.

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KKT and Weakly Complementary Approximate KKT Conditions for Interval-Valued Optimization Problems

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