Extremal points and optimal solutions for general capacity problems

This paper studies the infinite dimensional linear programming problems in the integration type. The variable is taken in the space of bounded regular Borel measures on compact Hausdorff spaces. It will find an optimal measure for a constrained optimization problem, namely a capacity problem. Relations between extremal points of the feasible region and optimal solutions of the optimization problem are investigated. The necessary/sufficient conditions for a measure to be optimal are establshed. The algorithm for optimal solution of the general capacity problem on X=Y=[0,1] is formulated.