A Necessary and Sufficient Condition for a Constrained Minimum

Let $U$ be an open subset of $\mathbb{R}^n $, $X$ a compact semi-analytic subset of $U$, $(f_0 ,f):U \to \mathbb{R} \times \mathbb{R}^n $ analytic, and $0 \in f(X)$. It is proven that a point $x_0 \in X$ minimizes $f_0 (x)$ subject to $f(x) = 0$ if and only if $x_0 \in X$ minimizes $f_0 (x) + c | {f...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on optimization Vol. 2; no. 4; pp. 665 - 667
Main Author Warga, J.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.11.1992
Subjects
Inequality
Optimization
Online AccessGet full text

Cover

More Information
Summary:Let $U$ be an open subset of $\mathbb{R}^n $, $X$ a compact semi-analytic subset of $U$, $(f_0 ,f):U \to \mathbb{R} \times \mathbb{R}^n $ analytic, and $0 \in f(X)$. It is proven that a point $x_0 \in X$ minimizes $f_0 (x)$ subject to $f(x) = 0$ if and only if $x_0 \in X$ minimizes $f_0 (x) + c | {f(x)} |^{1/N} $ for all sufficiently large $c$ and $N$. This reduces the constrained minimization problem to a finite number of unconstrained problems.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1052-6234
1095-7189
DOI:10.1137/0802033