Abstract Convexity and the Monge-Kantorovich Duality
作者： Vladimir L. Levin
DOI: 10.1007/978-3-540-37007-9_2
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摘要: In the present survey, we reveal links between abstract convex analysis and two variants of Monge-Kantorovich problem (MKP), with given marginals a marginal difference. It includes: (1) equivalence validity duality theorems for MKP appropriate convexity corresponding cost functions; (2) characterization (maximal) cyclic monotone map F: X → L ⊂ IRX in terms connected constraint set $$ Q_0 (\varphi ): = \{ u \in \mathbb{R}^z :u(z_1 ) - u(z_2 \leqslant \varphi (z_1 ,z_2 ){\text{ }}\forall z_1 ,z_1 Z dom{\text{ }}F\} $$ of particular dual difference L-subdifferentials L-convex (3) optimality criteria (and Monge problems) monotonicity non-emptiness Q 0(ϕ), where ϕ is special function on × determined by original c Y. The applied then to several problems mathematical economics relating utility theory, demand analysis, generalized dynamics optimization models, corruption, as well best approximation problem.
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