This paper mainly investigates the approximation of a global maximizer of the Monge–Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichl...This paper mainly investigates the approximation of a global maximizer of the Monge–Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary.Using an approximation mechanism,the primal maximization problem can be transformed into a sequence of minimization problems.By applying the systematic canonical duality theory,one is able to derive a sequence of analytic solutions for the minimization problems.In the final analysis,the convergence of the sequence to an analytical global maximizer of the primal Monge–Kantorovich problem will be demonstrated.展开更多
文摘This paper mainly investigates the approximation of a global maximizer of the Monge–Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary.Using an approximation mechanism,the primal maximization problem can be transformed into a sequence of minimization problems.By applying the systematic canonical duality theory,one is able to derive a sequence of analytic solutions for the minimization problems.In the final analysis,the convergence of the sequence to an analytical global maximizer of the primal Monge–Kantorovich problem will be demonstrated.
