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An Algorithm for Maximizing a Convex Function Based on Its Minimum

Author

Listed:
  • Aharon Ben-Tal

    (Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, Haifa 32000, Israel; Shenkar College, Ramat Gan 50200, Israel)

  • Ernst Roos

    (ORTEC, 2719 EA Zoetermeer, Netherlands)

Abstract

In this paper, an algorithm for maximizing a convex function over a convex feasible set is proposed. The algorithm, called CoMax, consists of two phases: in phase 1, a feasible starting point is obtained that is used in a gradient ascent algorithm in phase 2. The main contribution of the paper is connected to phase 1; five different methods are used to approximate the original NP-hard problem of maximizing a convex function (MCF) by a tractable convex optimization problem. All the methods use the minimizer of the convex objective function in their construction. In phase 2, the gradient ascent algorithm yields stationary points to the MCF problem. The performance of CoMax is tested on a wide variety of MCF problems, demonstrating its efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:6:p:3200-3214
    DOI: 10.1287/ijoc.2022.1238
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    References listed on IDEAS

    as
    1. Philip B. Zwart, 1974. "Global Maximization of a Convex Function with Linear Inequality Constraints," Operations Research, INFORMS, vol. 22(3), pages 602-609, June.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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