Second-Order Optimality Conditions with the Envelope-Like Effect for Set-Valued Optimization

P. Q. Khanh () and N. M. Tung ()
Additional contact information
P. Q. Khanh: International University, Vietnam National University Ho Chi Minh City
N. M. Tung: University of Science, Vietnam National University Ho Chi Minh City

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 1, No 4, 68-90

Abstract: Abstract We consider Karush–Kuhn–Tucker second-order optimality conditions for nonsmooth set-valued optimization with attention to the envelope-like effect. To analyse the critical feasible directions, which produce this phenomenon, we use the contingent derivatives, the adjacent derivatives and the corresponding asymptotic derivatives, since directions are explicitly involved in these kinds of derivatives. To pursue strong multiplier rules, we impose cone-Aubin conditions to deal with the objective and constraint maps separately. In this way, we can invoke constraint qualifications of the Kurcyusz–Robinson–Zowe type. To our knowledge, some of the results are new; they will be indicated explicitly. The paper also discusses improvements or extensions of known results.

Keywords: Optimality condition; Second-order contingent derivative; Kurcyusz–Robinson–Zowe constraint qualification; Weak minimizer; Firm minimizer; 90C29; 49J52; 90C46; 90C48 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0728-6 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:167:y:2015:i:1:d:10.1007_s10957-015-0728-6

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

DOI: 10.1007/s10957-015-0728-6

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 ().