Gradient descent procedure for solving linear programming relaxations of combinatorial optimization problems in parallel mode on extra large scale

Alexey Antonov

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arXiv · 2011.08170

Gradient descent procedure for solving linear programming relaxations of combinatorial optimization problems in parallel mode on extra large scale

Alexey Antonov

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Abstract

Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO problems. The algorithm can be run in parallel mode and was implemented as CUDA C/C++ program to be executed on GPU. We exemplify efficiency of the algorithm by solving a fractional 2-matching problem. Our results demonstrate that a fractional 2-matching problem with 100,000 nodes is solved by our algorithm on a modern GPU on a scale of a second while solving the problem with simplex method would take more than an hour. The algorithm can be modified to solve more complicated LP relaxations derived from CO problems.

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Alexey Antonov. 2020-11-16. Gradient descent procedure for solving linear programming relaxations of combinatorial optimization problems in parallel mode on extra large scale. https://arxiv.org/abs/2011.08170

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