A Dual Ascent Framework for Lagrangean Decomposition of Combinatorial Problems

TL;DR

This paper introduces a versatile dual ascent framework for Lagrangean decomposition that can be applied across various combinatorial problems, improving solution efficiency over existing methods.

Contribution

The authors develop a general dual ascent algorithm for Lagrangean decomposition applicable to multiple problem types, with parameter tuning for optimized performance.

Findings

Outperforms state-of-the-art solvers on graph matching problems

Effective on multicut problems, surpassing existing methods

Parameter tuning enhances algorithm efficiency

Abstract

We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to multiple problem types. In his work, we propose such a general algorithm. It depends on several parameters, which can be used to optimize its performance in each particular setting. We demonstrate efficacy of our method on graph matching and multicut problems, where it outperforms state-of-the-art solvers including those based on subgradient optimization and off-the-shelf linear programming solvers.