Characterizations of pseudoconvex functions and semistrictly quasiconvex ones

In this paper, we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke–Rockafellar subdifferential. Further, we extend to programs with pseudoconvex objective function two earlier...

Full description

Saved in:
Bibliographic Details
Published inJournal of global optimization Vol. 57; no. 3; pp. 677 - 693
Main Author Ivanov, Vsevolod I.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2013
Springer
Springer Nature B.V
Subjects
Computer Science
Constraints
Convex analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Pseudoconvex functions
Optimality conditions
Semistrictly quasiconvex functions
Nonsmooth analysis
90C46
Characterizations of the solution set of a set constrained optimization problem
90C26
26B25
Online AccessGet full text
ISSN0925-5001
1573-2916
DOI10.1007/s10898-012-9956-6

Cover

More Information
Summary:In this paper, we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke–Rockafellar subdifferential. Further, we extend to programs with pseudoconvex objective function two earlier characterizations of the solutions set of a set constrained nonlinear programming problem due to Mangasarian (Oper Res Lett 7:21–26, 1988 ). A positive function p appears in the most results. It is replaced by the number 1 if the function is convex and its domain of definition is convex, too.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9956-6