The notions of continuous ( strictly) pseudoconvex functions and set-valued ( strictly) pseudo-monotone maps are introduced. Relations between these notions are given using an asymptotic mean value theorem. Characteri...
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The notions of continuous ( strictly) pseudoconvex functions and set-valued ( strictly) pseudo-monotone maps are introduced. Relations between these notions are given using an asymptotic mean value theorem. Characterizations of a continuous quasiconvex function are derived.
In this paper, we study some problems with a continuously differentiable and quasiconvex objective function. We prove that exactly one of the following two alternatives holds: (I) the gradient of the objective functio...
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In this paper, we study some problems with a continuously differentiable and quasiconvex objective function. We prove that exactly one of the following two alternatives holds: (I) the gradient of the objective function is different from zero over the solution set, and the normalized gradient is constant over it;(II) the gradient of the objective function is equal to zero over the solution set. As a consequence, we obtain characterizations of the solution set of a program with a continuously differentiable and quasiconvex objective function, provided that one of the solutions is known. We also derive Lagrange multiplier characterizations of the solutions set of an inequality constrained problem with continuously differentiable objective function and differentiable constraints, which are all quasiconvex on some convex set, not necessarily open. We compare our results with the previous ones. Several examples are provided.
We study some classes of generalized affine functions, using a generalized differential. We study some properties and characterizations of these classes and we devise some characterizations of solution sets of optimiz...
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We study some classes of generalized affine functions, using a generalized differential. We study some properties and characterizations of these classes and we devise some characterizations of solution sets of optimization problems involving such functions or functions of related classes.
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