The convexity of the solution set of a pseudoconvex inequality

Zili Wu

doi:10.1016/j.na.2007.07.014

The convexity of the solution set of a pseudoconvex inequality

Zili Wu^*

^*Corresponding author for this work

Ninth Middle School (Jingu)

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

For a pseudoconvex function f on a nonempty convex set C in a real normed vector space X, we present several equivalent conditions for the convexity of the set C_x {colon equals} {c ∈ C : f (x) ≤ f (c)} for x ∈ C . These conditions turn out to be very useful in characterizing the solution set of a pseudoconvex minimization problem of f over C_x and the pseudolinearity of a Gâteux differentiable function f. We hence extend several existing results about characterizations of the solutions to a convex program and a pseudolinear program.

Original language	English
Pages (from-to)	1666-1674
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	69
Issue number	5-6
DOIs	https://doi.org/10.1016/j.na.2007.07.014
Publication status	Published - 1 Sept 2008
Externally published	Yes

Keywords

Characterizations of pseudolinearity
Convex solution sets
Pseudoconvex programs

Access to Document

10.1016/j.na.2007.07.014

Cite this

@article{b9e198daa47f482ea15300c151a26382,

title = "The convexity of the solution set of a pseudoconvex inequality",

abstract = "For a pseudoconvex function f on a nonempty convex set C in a real normed vector space X, we present several equivalent conditions for the convexity of the set Cx \{colon equals\} \{c ∈ C : f (x) ≤ f (c)\} for x ∈ C . These conditions turn out to be very useful in characterizing the solution set of a pseudoconvex minimization problem of f over Cx and the pseudolinearity of a G{\^a}teux differentiable function f. We hence extend several existing results about characterizations of the solutions to a convex program and a pseudolinear program.",

keywords = "Characterizations of pseudolinearity, Convex solution sets, Pseudoconvex programs",

author = "Zili Wu",

year = "2008",

month = sep,

day = "1",

doi = "10.1016/j.na.2007.07.014",

language = "English",

volume = "69",

pages = "1666--1674",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

number = "5-6",

}

TY - JOUR

T1 - The convexity of the solution set of a pseudoconvex inequality

AU - Wu, Zili

PY - 2008/9/1

Y1 - 2008/9/1

N2 - For a pseudoconvex function f on a nonempty convex set C in a real normed vector space X, we present several equivalent conditions for the convexity of the set Cx {colon equals} {c ∈ C : f (x) ≤ f (c)} for x ∈ C . These conditions turn out to be very useful in characterizing the solution set of a pseudoconvex minimization problem of f over Cx and the pseudolinearity of a Gâteux differentiable function f. We hence extend several existing results about characterizations of the solutions to a convex program and a pseudolinear program.

AB - For a pseudoconvex function f on a nonempty convex set C in a real normed vector space X, we present several equivalent conditions for the convexity of the set Cx {colon equals} {c ∈ C : f (x) ≤ f (c)} for x ∈ C . These conditions turn out to be very useful in characterizing the solution set of a pseudoconvex minimization problem of f over Cx and the pseudolinearity of a Gâteux differentiable function f. We hence extend several existing results about characterizations of the solutions to a convex program and a pseudolinear program.

KW - Characterizations of pseudolinearity

KW - Convex solution sets

KW - Pseudoconvex programs

UR - https://www.scopus.com/pages/publications/44649129996

U2 - 10.1016/j.na.2007.07.014

DO - 10.1016/j.na.2007.07.014

M3 - Article

AN - SCOPUS:44649129996

SN - 0362-546X

VL - 69

SP - 1666

EP - 1674

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 5-6

ER -

The convexity of the solution set of a pseudoconvex inequality

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this