Continuous Equality Knapsack with Probit-Style Objectives

Jamie Fravel (), Robert Hildebrand () and Laurel Travis
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Jamie Fravel: Virginia Tech
Robert Hildebrand: Virginia Tech
Laurel Travis: Virginia Tech

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 3, 1060-1076

Abstract: 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.

Date: 2024
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DOI: 10.1007/s10957-024-02503-5

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