Book ChapterDOI
Topics in the Duality Theory for Mass Transfer Problems
V. L. Levin
- pp 243-252
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Duality theory for nontopological versions of mass transfer problem extending the classical Monge-Kantorovich problem is developed in this paper, where applications to dynamic optimization and approximation theory are outlined.Abstract:
Duality theory for nontopological versions of mass transfer problem extending the classical Monge-Kantorovich problem is developed. Applications to dynamic optimization and approximation theory are outlined.read more
Citations
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Journal ArticleDOI
Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem
TL;DR: In this paper, a criterion for a multivalued operator F : X → L, where L \( \subseteq\)RX is obtained and connections with the notions of L-convex function and of its L-subdifferentials are established.
Book ChapterDOI
Optimal solutions of the Monge problem
TL;DR: In this paper, the optimality conditions for Monge solutions of the Monge-Kantorovich problem with a smooth cost function were obtained for several natural classes of cost functions.
Journal ArticleDOI
Abstract Convexity in Measure Theory and in Convex Analysis
TL;DR: In this article, Levin et al. discuss the existence of convexity in measure-theoretic theory and in CONVEX ANALYSIS, and propose a solution.
Book ChapterDOI
Abstract Convexity and the Monge-Kantorovich Duality
TL;DR: In this article, the authors reveal links between abstract convex analysis and two variants of the Monge-Kantorovich problem (MKP), with given marginals and with a given marginal difference.
Book ChapterDOI
A method in demand analysis connected with the Monge—Kantorovich problem
TL;DR: In this article, a method in demand analysis based on the Monge-Kantorovich duality is developed, which characterizes demand functions that are rationalized by concave utility functions with some additional properties such as upper semi-continuity, continuity, non-decrease, strict concavity, positive homogeneity and so on.
References
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Journal ArticleDOI
The problem of mass transfer with a discontinuous cost function and a mass statement of the duality problem for convex extremal problems
V L Levin,A A Milyutin +1 more
TL;DR: In this article, the abstract version of Problems A and B with cost function satisfying the triangle inequality is presented, and its generalization to non-metrizable compact spaces is discussed.
Journal ArticleDOI
Reduced cost functions and their applications
TL;DR: In this paper, the authors examined the properties of reduced cost functions and closely related sets Q 0 (c) in a more general setting than before, viz demand theory, rationalizability of action profiles in a principal-agent framework, and optimality of trajectories in dynamic optimization problems.
Journal ArticleDOI
Some applications of set-valued mappings in mathematical economics
TL;DR: In this paper, a characterization of preferences R:X → 2 X that admit d -Lipschitz utility functions is presented, and the asymptotic behavior of a dynamical system determined by R is another subject of study.
Journal ArticleDOI
A superlinear multifunction arising in connection with mass transfer problems
TL;DR: In this paper, the authors studied properties of the multifunction including conditions on c for Q 0(c) to be nonempty and characterizations of Q 0 (c) for a given c. Applications are given to cyclically monotone operators and to dynamic optimization.