The use of pseudo-convexity and quasi-convexity in sufficient conditions for global constrained extrema†

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Abstract
Several sufficient conditions for global constrained minima are given. These conditions consist of necessary conditions for local minima together with generalized convexity assumptions. The eonvexity-type assumptions are made on the Lagrangian function, which presents the advantage of not requiring any (generalized convexity) assumption on each function involved in the problem and of allowing problems with several local extrema. Previously obtained results are used to replace pseudo-convexity by a more workable condition.

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