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Continuous Equality Knapsack with Probit-Style Objectives

Author

Listed:
  • Jamie Fravel

    (Virginia Tech)

  • Robert Hildebrand

    (Virginia Tech)

  • Laurel Travis

    (Virginia Tech)

Abstract

We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function.

Suggested Citation

  • Jamie Fravel & Robert Hildebrand & Laurel Travis, 2024. "Continuous Equality Knapsack with Probit-Style Objectives," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1060-1076, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02503-5
    DOI: 10.1007/s10957-024-02503-5
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