\((\Phi_ 1,\Phi_ 2)\) 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.


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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