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F. A. Valentine, “The Problem of Lagrange with Differentiable Inequalities as Side Consrtaints, Contribution to the Calculus of Variation 1933-1937,” University of Chicago Press, Chicago, 1937, pp. 407-448.

has been cited by the following article:

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

  AUTHORS: Mourad Naffouti

  KEYWORDS: Optimality Conditions; Constraint Qualifications; Copositivity

  JOURNAL NAME: Open Journal of Optimization, Vol.2 No.4, December 3, 2013

  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.