区间值优化问题的 KKT 和弱互补近似 KKT 条件

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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References 22

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

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