On an extended lagrange claim

Liqun Qi

doi:10.1023/A:1017547727539

On an extended lagrange claim

Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

4 Citations (Scopus)

Abstract

Lagrange once made a claim having the consequence that a smooth function f has a local minimum at a point if all the directional derivatives of f at that point are nonnegative. That the Lagrange claim is wrong was shown by a counterexample given by Peano. In this note, we show that an extended claim of Lagrange is right. We show that, if all the lower directional derivatives of a locally Lipschitz function f at a point are positive, then f has a strict minimum at that point.

Original language	English
Pages (from-to)	685-688
Number of pages	4
Journal	Journal of Optimization Theory and Applications
Volume	108
Issue number	3
DOIs	https://doi.org/10.1023/A:1017547727539
Publication status	Published - 1 Mar 2001

Keywords

Directional derivatives
Lipschitz continuous functions
Minimum points

ASJC Scopus subject areas

Management Science and Operations Research
Applied Mathematics
Control and Optimization

More information

10.1023/A:1017547727539

Cite this

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KW - Minimum points

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On an extended lagrange claim

Abstract

Keywords

ASJC Scopus subject areas

More information

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