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\((\Phi , \rho )\)-invexity in nonsmooth optimization. (English) Zbl 1229.90133

Authors’ abstract: “In this article, a new class of nonconvex nondifferentiable functions, called locally Lipschitz \((\Phi , \rho )\)-invex functions, being introduced, includes many well known classes of nondifferentiable generalized convex functions as its subclasses. Some properties of the introduced class of locally Lipschitz \((\Phi , \rho )\)-invex functions are studied. Further, nonsmooth mathematical programming problems involving locally Lipschitz \((\Phi , \rho )\)-invex functions are considered. Optimality and Mond-Weir duality results for such a class of nonsmooth optimization problems are established.”

MSC:

90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
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