On the Second Order Optimality Conditions for Optimization Problems with Inequality Constraints

Mourad Naffouti

Department of Mathematics, Faculty of Science, Mathematics, Physics and Natural of Tunis, Tunis, Tunisia.

DOI: 10.4236/ojop.2013.24014                

Abstract

A nonlinear optimization problem (P) with inequality constraints can be converted into a new optimization problem (PE) with equality constraints only. This is a Valentine method for finite dimensional optimization. We review second order optimality conditions for (PE) in connection with those of (P). A strictly complementary slackness condition can be made to get the property that sufficient optimality conditions for (P) imply the same property for (PE). We give some new results (see Theorems 3.1, 3.2 and 3.3) .Without any assumption, a counterexample is given to show that these conditions are not equivalent.

Keywords

Optimality Conditions; Constraint Qualifications; Copositivity

Conflicts of Interest

The authors declare no conflicts of interest.

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