Work

New finite relaxation hierarchies for concavo-convex, disjoint bilinear programs, and facial disjunctions

Year: 2026

Type: article

Abstract: This paper introduces novel relaxation hierarchies for concavo-convex programs (CXP), a class of problems that includes disjoint bilinear programming (DBP) and concave minimization (CM) as special cases. At the core of these hierarchies is an algorithm based on double-description (DD) that computes the barycentric coordinates of a polyhedral cone as rational, non-negative functions representing multipliers associated with the cone’s rays. These hierarchies combine geometric structure derived from barycentric coordinates with algebraic techniques via rational functions, achieving the convex hull in m iterations, where m is the number of inequalities that a subset of the variables must satisfy. Our framework offers the first unified approach to analyze and tighten relaxations from disjunctive programming (DP) and reformulation-linearization technique (RLT) for CXP. We also demonstrate that our methods extend to facial disjunctive programs (FDP), where solutions are constrained to lie on faces of a Cartesian product of polytopes, generalizing known hierarchies for 0-1 programs.

Source: Mathematical Programming

DOI: 10.1007/s10107-026-02326-4

Author: Mohit Tawarmalani

Institution: Purdue University West Lafayette

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Air Force Research Laboratory