Continuous Equality Knapsack with Probit-Style Objectives
Optimization and Control
2024-07-16 v2
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.
Cite
@article{arxiv.2211.02237,
title = {Continuous Equality Knapsack with Probit-Style Objectives},
author = {Jamie Fravel and Robert Hildebrand and Laurel Travis},
journal= {arXiv preprint arXiv:2211.02237},
year = {2024}
}