Extremal Points and an Algorithm for a Class of Continuous Transportation Problems

An algorithm for semi-infinite transportation problems

“…From Wu [13], we know if s * (y) is continuous on Y and r * i + s * (y) c(x i , y) for i = 1, 2, . .…”

“…A large number of papers [1,2,[4][5][6][7][8][9][10][11]13] have appeared in the literature on this problem. They have mostly been concerned with the duality theory of the CTP and the existence of optimal solutions for such a problem.…”

“…They have mostly been concerned with the duality theory of the CTP and the existence of optimal solutions for such a problem. Only a few of papers [1,2,10,11,13] discuss the algorithms for some special classes of CTPs.…”

“…Anderson and Nash [1] and Lewis [10] discussed the semi-finite TP, which has some relation to the version of our problem. From Wu [13], we know the CTP has an optimal solution at an extreme point of the feasible region. Anderson and Nash [1] proved that there is an optimal solution for DCTP.…”

Strong duality of the Monge-Kantorovich mass transfer problem in metric spaces

“…In contrast, in the standard formulation of infinite-dimentional LP problems the underlying vector spaces are given at the outset, and so the cost function is automatically restricted. Thus most of the literature that uses the LP approach -for instance [2,15,28] -is almost necessarily concentrated on the MT problem with compact spaces X, Y and/or a bounded cost function c.…”