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Global Maximization of a Convex Function with Linear Inequality Constraints

Author

Listed:
  • Philip B. Zwart

    (Washington University, St. Louis, Missouri)

Abstract

This paper presents an algorithm for the global maximization of a convex function subject to linear inequality constraints. It is computationally finite and is designed to converge rapidly on problems in which there are few local optima or the global optimum is significantly better than most of the other local optima.

Suggested Citation

  • Philip B. Zwart, 1974. "Global Maximization of a Convex Function with Linear Inequality Constraints," Operations Research, INFORMS, vol. 22(3), pages 602-609, June.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:3:p:602-609
    DOI: 10.1287/opre.22.3.602
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    Cited by:

    1. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. Ankhili, Z. & Mansouri, A., 2009. "An exact penalty on bilevel programs with linear vector optimization lower level," European Journal of Operational Research, Elsevier, vol. 197(1), pages 36-41, August.
    3. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    4. B. Jaumard & C. Meyer, 2001. "On the Convergence of Cone Splitting Algorithms with ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 119-144, July.
    5. Pooriya Beyhaghi & Thomas R. Bewley, 2016. "Delaunay-based derivative-free optimization via global surrogates, part II: convex constraints," Journal of Global Optimization, Springer, vol. 66(3), pages 383-415, November.
    6. Aharon Ben-Tal & Ernst Roos, 2022. "An Algorithm for Maximizing a Convex Function Based on Its Minimum," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3200-3214, November.
    7. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    8. Aras Selvi & Aharon Ben-Tal & Ruud Brekelmans & Dick den Hertog, 2022. "Convex Maximization via Adjustable Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2091-2105, July.
    9. Roos, Ernst, 2021. "Robust approaches for optimization problems with convex uncertainty," Other publications TiSEM dd9e7b35-a770-4f8d-a85c-8, Tilburg University, School of Economics and Management.
    10. Queiroz, Marcelo & Humes, Carlos, 2003. "A heuristic for the continuous capacity and flow assignment," European Journal of Operational Research, Elsevier, vol. 146(3), pages 444-459, May.

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