New finite relaxation hierarchies for concavo-convex, disjoint bilinear programs, and facial disjunctions
Mohit Tawarmalani
What the paper says
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.
Evidence weight
Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40
| F · citation impact | 0.50 × 0.4 = 0.20 |
| M · momentum | 0.50 × 0.15 = 0.07 |
| V · venue signal | 0.50 × 0.05 = 0.03 |
| R · text relevance † | 0.50 × 0.4 = 0.20 |
† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.