Optimality Conditions and Characterizations of the Solution Sets in Generalized Convex Problems and Variational Inequalities

Vsevolod I. Ivanov ()
Additional contact information
Vsevolod I. Ivanov: Technical University of Varna

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 1, No 4, 65-84

Abstract: Abstract We derive necessary and sufficient conditions for optimality of a problem with a pseudoconvex objective function, provided that a finite number of solutions are known. In particular, we see that the gradient of the objective function at every minimizer is a product of some positive function and the gradient of the objective function at another fixed minimizer. We apply this condition to provide several complete characterizations of the solution sets of set-constrained and inequality-constrained nonlinear programming problems with pseudoconvex and second-order pseudoconvex objective functions in terms of a known solution. Additionally, we characterize the solution sets of the Stampacchia and Minty variational inequalities with a pseudomonotone-star map, provided that some solution is known.

Keywords: Global optimization; Pseudoconvex function; Variational inequality; Pseudomonotone-star map (search for similar items in EconPapers)
Date: 2013
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/s10957-012-0243-y 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:158:y:2013:i:1:d:10.1007_s10957-012-0243-y

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

DOI: 10.1007/s10957-012-0243-y

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 ().