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arXiv · 2211.02237

Continuous Equality Knapsack with Probit-Style Objectives

Jamie Fravel·Robert Hildebrand·Laurel Travis
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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.

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Jamie Fravel, Robert Hildebrand, Laurel Travis. 2022-11-04. Continuous Equality Knapsack with Probit-Style Objectives. https://arxiv.org/abs/2211.02237

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