Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1012.49014
Studniarski, Marcin
On weak sharp minima for a special class of nonsmooth functions. (English)
[J] Discuss. Math., Differ. Incl. Control Optim. 20, No.2, 195-207 (2000). ISSN 1509-9407; ISSN 2084-0365/e

Let $f: \bbfR^n\to [-\infty,+\infty]$ be a function which is finite and constant on a set $S\subseteq \bbfR^n$. A point $\overline x\in S$ is called weak sharp local minimizer of order $m$ for $f$ if there exist $\beta> 0$ and $\varepsilon> 0$ such that $$f(x)- f(\overline x)\ge \beta(\text{dist}(x, S))^m\quad\text{for all }x\in B(\overline x,\varepsilon),$$ where $\text{dist}(x,S)$ is the distance of $x$ from $S$. The main result of the paper is a characterization of weak sharp local minimizers of order 1 for a function $f$ which is a finite maximum of strictly differentiable functions. The characterization makes use of the Mordukhovich normal cone to $S$. The result is then applied to a smooth constrained optimization problem.
[N.Hadjisavvas (Karlovassi)]

MSC 2000:: *49J52 Nonsmooth analysis (other weak concepts of optimality)
49K35 Minimax problems (necessity and sufficiency)

Keywords: weak sharp local minimizers; strictly differentiable functions; Mordukhovich normal cone

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]