A Necessary and Sufficient Condition for a Constrained Minimum

• Published in: SIAM journal on optimization Vol. 2; no. 4; pp. 665 - 667
• Main Author: Warga, J.
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.11.1992
• Subjects: Inequality; Optimization

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...