On an Extended Lagrange Claim

L Qi
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L Qi: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2001, vol. 108, issue 3, No 12, 685-688

Abstract: 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.

Keywords: Minimum points; directional derivatives; Lipschitz continuous functions (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017547727539

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