We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a plan between two marginals that are probability measures on compact subsets of Euclidean space. consider case regularization with negative entropy respect to Lebesgue measure, which has attracted attention because it can be solved by very simple Sinkhorn algorithm. first regularized problem conte...

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

we introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...

this paper offers an approach that could be useful for diverse types of layout problems or even area allocation problems. by this approach there is no need to large number of discrete variables and only by few continues variables large-scale layout problems could be solved in polynomial time. this is resulted from dividing area into discrete and continuous dimensions. also defining decision var...

We introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...