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Extremal points and optimal solutions for general capacity problems

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Abstract

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 established. The algorithm for optimal solution of the general capacity problem onX = Y = [0, 1] is formulated.

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Authors and Affiliations

  1. Department of Mathematics, University of Cape Town, Cape Town, South Africa

    H. C. Lai

  2. Institute of Applied Mathematics, National Cheng-Kung University, Tainan, Taiwan, ROC

    S. Y. Wu

Authors
  1. H. C. Lai
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  2. S. Y. Wu
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Lai, H.C., Wu, S.Y. Extremal points and optimal solutions for general capacity problems. Mathematical Programming 54, 87–113 (1992). https://doi.org/10.1007/BF01586043

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  • DOI: https://doi.org/10.1007/BF01586043

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