# Half-quadratic transportation problems

## TL;DR

This paper introduces a memory-efficient primal-dual algorithm for solving relaxed, differentiable transportation problems by approximating the cost function with weighted quadratic problems, enabling solutions to non-convex cases.

## Contribution

It proposes a novel approach that approximates the transportation problem with a differentiable cost, allowing for efficient solutions to non-convex problems.

## Key findings

- Efficient memory usage in solving transportation problems.
- Ability to handle non-convex, differentiable cost functions.
- Approximation method via weighted quadratic transportation problems.

## Abstract

We present a primal--dual memory efficient algorithm for solving a relaxed version of the general transportation problem. Our approach approximates the original cost function with a differentiable one that is solved as a sequence of weighted quadratic transportation problems. The new formulation allows us to solve differentiable, non-- convex transportation problems.