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Black-Box Acceleration of Monotone Convex Program Solvers

Author

Listed:
  • Palma London

    (California Institute of Technology, Pasadena, California 91125)

  • Shai Vardi

    (Purdue University, West Lafayette, Indiana 47907)

  • Reza Eghbali

    (University of California, Berkeley, California 94720)

  • Adam Wierman

    (California Institute of Technology, Pasadena, California 91125)

Abstract

This paper presents a black-box framework for accelerating packing optimization solvers. Our method applies to packing linear programming problems and a family of convex programming problems with linear constraints. The framework is designed for high-dimensional problems, for which the number of variables n is much larger than the number of measurements m . Given an ( m × n ) problem, we construct a smaller ( m × ϵ n ) problem, whose solution we use to find an approximation to the optimal solution. Our framework can accelerate both exact and approximate solvers. If the solver being accelerated produces an α -approximation, then we produce a ( 1 − ϵ ) / α 2 -approximation of the optimal solution to the original problem. We present worst-case guarantees on run time and empirically demonstrate speedups of two orders of magnitude.

Suggested Citation

  • Palma London & Shai Vardi & Reza Eghbali & Adam Wierman, 2024. "Black-Box Acceleration of Monotone Convex Program Solvers," Operations Research, INFORMS, vol. 72(2), pages 796-815, March.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:2:p:796-815
    DOI: 10.1287/opre.2022.2352
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