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\((\Phi_ 1,\Phi_ 2)\) optimality and duality under differentiability. (English) Zbl 0883.90114

Summary: \((\Phi_1,\Phi_2)\)-convexity is applied to develop optimality conditions of Fritz John type and Kuhn-Tucker type under differentiability for a minimization problem with real-valued objective and inequality constraints. A dual of the Mond-Weir type is considered and a number of weak and strong duality results are established. Weak and strong duality theorems are also given in the framework of Wolfe duality.

MSC:

90C30 Nonlinear programming
26B25 Convexity of real functions of several variables, generalizations
52A40 Inequalities and extremum problems involving convexity in convex geometry
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References:

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