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August, 2018 Existence and Boundedness of Second-order Karush-Kuhn-Tucker Multipliers for Set-valued Optimization with Variable Ordering Structures
Quoc Khanh Phan, Minh Tung Nguyen
Taiwanese J. Math. 22(4): 1001-1029 (August, 2018). DOI: 10.11650/tjm/180505

Abstract

In this paper we investigate second-order Karush-Kuhn-Tucker multipliers for both local nondominated and local minimal points of set-valued optimization with variable ordering structures. We prove calculus rules of second-order contingent derivatives of index $\gamma \in \{0,1\}$ and use them to establish improved Karush-Kuhn-Tucker multiplier rules of nonclassical forms which involve separately such derivatives of the objective, constraint and ordering maps. The equivalence between the nonemptiness and boundedness of the multiplier sets in these rules and second-order constraint qualifications of the Kurcyusz-Robinson-Zowe and Mangasarian-Fromovitz types is demonstrated.

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Quoc Khanh Phan. Minh Tung Nguyen. "Existence and Boundedness of Second-order Karush-Kuhn-Tucker Multipliers for Set-valued Optimization with Variable Ordering Structures." Taiwanese J. Math. 22 (4) 1001 - 1029, August, 2018. https://doi.org/10.11650/tjm/180505

Information

Received: 20 September 2017; Revised: 25 March 2018; Accepted: 20 May 2018; Published: August, 2018
First available in Project Euclid: 9 June 2018

zbMATH: 06965407
MathSciNet: MR3830831
Digital Object Identifier: 10.11650/tjm/180505

Subjects:
Primary: 49J52 , 49J53 , 90C30 , 90C46

Keywords: constraint qualification , contingent derivative of index $\gamma$ , nondominated point , second-order KKT multiplier , variable ordering structure

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

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Vol.22 • No. 4 • August, 2018
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