Cutting plane algorithms for nonlinear binary optimization

TL;DR

This paper introduces a cutting plane approach for solving nonlinear, nonconvex binary optimization problems, providing convergence analysis and dual optimality conditions, expanding the scope beyond convex settings.

Contribution

It presents a novel cutting plane algorithm with rigorous convergence guarantees for nonlinear binary optimization, including nonconvex cases, and derives dual optimality conditions using variational analysis.

Findings

Convergence analysis quantifies iteration bounds under various conditions.

The method extends discrete optimization techniques to nonconvex problems.

Necessary and sufficient dual optimality conditions are established.

Abstract

Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary optimization problems. We provide a rigorous convergence analysis that quantifies the number of iterations required under different conditions. This is different to most other work in discrete optimization where only finite convergence is proved. Moreover, using tools from variational analysis, we provide necessary and sufficient dual optimality conditions.