On the Classical Necessary Second-Order Optimality Conditions

A. Baccari
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A. Baccari: Ecole Supérieure des Sciences et Techniques de Tunis

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 1, No 10, 213-221

Abstract: Abstract In this paper, the property of a necessary second-order optimality condition to hold with the same Lagrange multiplier for all critical vectors is investigated. It is limited to nonconvex optimization Problems in ℝn with equality and inequality constraints; the Mangasarian-Fromovitz constraint qualification is assumed to be hold. A counterexample was given recently by Anitescu. We give some sufficient conditions and we prove that this property holds if n ≤ 2 or if the number of active inequality constraints is at most two. For three active inequality constraints and n =3, a counterexample is given.

Keywords: Nonconvex optimization; Lagrange multipliers; pairs of quadratic forms; Mangasarian-Fromovitz constraint qualification (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (8)

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DOI: 10.1023/B:JOTA.0000043998.04008.e6

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