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An Exact Algorithm Based on the Kuhn–Tucker Conditions for Solving Linear Generalized Semi-Infinite Programming Problems

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  • Abraham Barragán
  • José-Fernando Camacho-Vallejo
  • Ram Jiwari

Abstract

Optimization problems containing a finite number of variables and an infinite number of constraints are called semi-infinite programming problems. Under certain conditions, a class of these problems can be represented as bi-level programming problems. Bi-level problems are a particular class of optimization problems, in which there is another optimization problem embedded in one of the constraints. We reformulate a semi-infinite problem into a bi-level problem and then into a single-level nonlinear one by using the Kuhn–Tucker optimality conditions. The resulting reformulation allows us to employ a branch and bound scheme to optimally solve the problem. Computational experimentation over well-known instances shows the effectiveness of the developed method concluding that it is able to effectively solve linear semi-infinite programming problems. Additionally, some linear bi-level problems from literature are used to validate the robustness of the proposed algorithm.

Suggested Citation

  • Abraham Barragán & José-Fernando Camacho-Vallejo & Ram Jiwari, 2022. "An Exact Algorithm Based on the Kuhn–Tucker Conditions for Solving Linear Generalized Semi-Infinite Programming Problems," Journal of Mathematics, Hindawi, vol. 2022, pages 1-14, April.
    • Handle: RePEc:hin:jjmath:1765385
    DOI: 10.1155/2022/1765385
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