First order characterizations of pseudoconvex functions (Q2761692)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: First order characterizations of pseudoconvex functions |
scientific article; zbMATH DE number 1686260
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | First order characterizations of pseudoconvex functions |
scientific article; zbMATH DE number 1686260 |
Statements
9 January 2002
0 references
generalized convexity
0 references
pseudoconvex function
0 references
quasiconvex function
0 references
directional derivative
0 references
0.93623316
0 references
0.91205347
0 references
0 references
0 references
0.8866263
0 references
First order characterizations of pseudoconvex functions (English)
0 references
In this paper the author proposes a generalization of the notion of pseudoconvexity given by Mangasarian for differentiable functions by replacing the (directional) derivative by an appropriate abstract function. Under certain conditions on this abstract ``derivative'', characterizations of this notion of pseudoconvexity are obtained. As a natural consequence first order optimality conditions for such functions are proved. Another application is a criterion for a quasiconvex function to be pseudoconvex. Finally, monotone type properties of the abstract derivatives are studied.
0 references
