Characterizations of Solution Sets of Differentiable Quasiconvex Programming Problems

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

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 1, No 7, 144-162

Abstract: Abstract In this paper, we study some problems with a continuously differentiable and quasiconvex objective function. We prove that exactly one of the following two alternatives holds: (I) the gradient of the objective function is different from zero over the solution set, and the normalized gradient is constant over it; (II) the gradient of the objective function is equal to zero over the solution set. As a consequence, we obtain characterizations of the solution set of a program with a continuously differentiable and quasiconvex objective function, provided that one of the solutions is known. We also derive Lagrange multiplier characterizations of the solutions set of an inequality constrained problem with continuously differentiable objective function and differentiable constraints, which are all quasiconvex on some convex set, not necessarily open. We compare our results with the previous ones. Several examples are provided.

Keywords: Quasiconvex function; Characterizations of the solution set; Quasiconvex program; Pseudoconvex function; KKT Conditions; 90C26; 26B25; 90C46 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1379-1 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:181:y:2019:i:1:d:10.1007_s10957-018-1379-1

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

DOI: 10.1007/s10957-018-1379-1

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 ().