Related papers: Quasidifferentials in Kantorovich Spaces
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…
This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric…
This paper is concerned with an optimization problem governed by the Kantorovich optimal transportation problem. This gives rise to a bilevel optimization problem, which can be reformulated as a mathematical problem with complementarity…
This paper is concerned with an optimization problem that is constrained by the Kantorovich optimal transportation problem. This bilevel optimization problem can be reformulated as a mathematical problem with complementarity constraints in…
The purpose of this work is to investigate root finding problems defined on (quasi-)metric spaces, and ranging in Euclidean spaces. The motivation for this line of inquiry stems from recent models in biology and phylogenetics, where…
We consider symmetric multi-marginal Kantorovich optimal transport problems on finite state spaces with uniform-marginal constraint. These problems consist of minimizing a linear objective function over a high-dimensional polytope, here…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric…
As the title suggests, this is the third paper in a series addressing bilevel optimization problems that are governed by the Kantorovich problem of optimal transport. These tasks can be reformulated as mathematical problems with…
The aim of the present paper is to extend Kantorovich's mass transport problem to the framework of upper/lower continuous capacities and to prove the cyclic monotonicity of the supports of optimal supermodular plans. As in the probabilistic…
Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…
We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus we extend the theory of the…
We study regression problems with distribution-valued responses and mixed distributional and Euclidean predictors. In quadratic cost, the negative gradient of the Kantorovich potential represents, at each source location, the displacement…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
In mathematical economics, the used functions are, in general, considered to be quasiconcave. Moreover, they are, in many cases, separable of nature. It is known that a local maximum of a quasiconcave function is not, in general, a global…
In this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of continuity in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative…
This paper studies the uniqueness of solutions to the dual optimal transport problem, both qualitatively and quantitatively (bounds on the diameter of the set of optimisers). On the qualitative side, we prove that when one marginal…
Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix…
The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in…