Generalized convex relations with applications to optimization and models of economic dynamics |
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| Authors: | A M Rubinov V Jeyakumar and B M Glover |
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| Institution: | (1) Department of Mathematics and Computing Sciences, Ben Gurion University of the Negev, Israel;(2) School of Mathematics, University of New South Wales, 2052 Sydney, Australia;(3) School of Information Technology and Mathematical Sciences, University of Ballarat, 3353 Ballarat, Australia |
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| Abstract: | We examine a notion of generalized convex set-valued mapping, extending the notions of a convex relation and a convex process. Under general conditions, we establish duality results for composite set-valued mappings and for convex programming problems involving convex set-valued mappings. We also present applications to the study of economic dynamical systems, by obtaining the characteristics of optimal paths generated by convex processes, and to optimization problems of a certain class of positively homogeneous increasing functions. |
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| Keywords: | 90C30 49B27 90C48 |
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