# Continuous Equality Knapsack with Probit-Style Objectives

arXiv: https://arxiv.org/abs/2211.02237 · HTML: https://mlsanity.com/paper/2211.02237/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding](https://mlsanity.com/paper/2512.20682/) (2025)

## Abstract (arXiv)

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.