On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization

Min Feng (), Shengjie Li () and Jie Wang ()
Additional contact information
Min Feng: Chongqing Jiaotong University
Shengjie Li: Chongqing University
Jie Wang: Chongqing University

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 2, No 5, 480-503

Abstract: Abstract This paper concentrates on necessary conditions for properly efficient solutions in nonsmooth multiobjective optimization problems. We first present a generalization of Tucker’s alternative theorem for conic nonlinear systems, provided that a closedness condition holds. Some sufficient conditions for the validity of such a closedness condition are given. As applications, under the weak Abadie regularity condition, we then establish the primal and the strong Karush/Kuhn–Tucker (dual) necessary optimality conditions for an efficient solution to be locally properly efficient in Borwein’s sense. The primal and the dual conditions are formulated as an equivalent pair by means of the Tucker-type alternative results. Finally we give an example to illustrate that Borwein’s locally properly efficient solution cannot be reduced to the only efficient one in the main results.

Keywords: Nonsmooth multiobjective optimization; Theorems of the alternative; Properly efficient solutions; Weak regularity conditions; Strong Karush/Kuhn–Tucker conditions; 26A27; 49K99; 90C29 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-022-02092-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02092-1

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-022-02092-1

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().