Taiwanese Journal of Mathematics

Existence and Boundedness of Second-order Karush-Kuhn-Tucker Multipliers for Set-valued Optimization with Variable Ordering Structures

Quoc Khanh Phan and Minh Tung Nguyen

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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.

Article information

Taiwanese J. Math., Volume 22, Number 4 (2018), 1001-1029.

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

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Zentralblatt MATH identifier

Primary: 90C30: Nonlinear programming 90C46: Optimality conditions, duality [See also 49N15] 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56] 49J53: Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]

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


Phan, Quoc Khanh; Nguyen, Minh Tung. Existence and Boundedness of Second-order Karush-Kuhn-Tucker Multipliers for Set-valued Optimization with Variable Ordering Structures. Taiwanese J. Math. 22 (2018), no. 4, 1001--1029. doi:10.11650/tjm/180505. https://projecteuclid.org/euclid.twjm/1528509853

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