Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/23392
Title: On an extended lagrange claim
Authors: Qi, L 
Keywords: Directional derivatives
Lipschitz continuous functions
Minimum points
Issue Date: 2001
Publisher: Springer
Source: Journal of optimization theory and applications, 2001, v. 108, no. 3, p. 685-688 How to cite?
Journal: Journal of optimization theory and applications 
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.
URI: http://hdl.handle.net/10397/23392
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1023/A:1017547727539
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