Work

On Cutting Plane Algorithms for Nonlinear Binary Optimization

Year: 2025

Type: article

Abstract: . The cutting plane method is known to converge for concave discrete maximization problems. This paper introduces a new condition for convergence that is weaker than concavity, allowing for extensions to generalized concave cases such as quasiconcavity and pseudoconcavity. More significantly, the new convergence condition enables the use of smaller penalty values in the standard concave reformulation technique for general nonconcave problems, yielding stronger cuts and faster convergence. In concave cases, this condition can even be applied to “deconcavify” concave problems to enhance convergence speed. Numerical results show that exploiting the new convergence condition can yield substantial computational improvements for complex, large-scale discrete optimization problems with up to one thousand variables.

Source: SIAM Journal on Optimization

DOI: 10.1137/23m1592493

Authors: Hoa T. Bui, Ryan Loxton, Qun Lin

Institution: Curtin University

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Australian Education International, Australian Government, Government of Western Australia, Australian Research Council

Award: ARC Training Centre for Transforming Maintenance through Data Science