论文信息 - Cliques for Multi-Term Linearization of 0-1 Multilinear Program for Boolean Logical Pattern Generation

Cliques for Multi-Term Linearization of 0-1 Multilinear Program for Boolean Logical Pattern Generation

0–1 multilinear program (MP) holds a unifying theory to Boolean logical pattern generation. For a tighter polyhedral relaxation of MP, this note exploits cliques in the graph representation of data under analysis to generate valid inequalities for MP that subsume all previous results and, collectively, provide a much stronger relaxation of MP. A preliminary numerical study demonstrates strength and practical benefits of the new results.

Hong Seo Ryoo | Kedong Yan

[1] Alberto Del Pia,et al. The Multilinear Polytope for Acyclic Hypergraphs , 2018, SIAM J. Optim..

[2] Hong Seo Ryoo,et al. A multi-term, polyhedral relaxation of a 0–1 multilinear function for Boolean logical pattern generation , 2019, J. Glob. Optim..

[3] Anatoliy D. Rikun,et al. A Convex Envelope Formula for Multilinear Functions , 1997, J. Glob. Optim..

[4] Alberto Del Pia,et al. A Polyhedral Study of Binary Polynomial Programs , 2017, Math. Oper. Res..

[5] Hong Seo Ryoo,et al. 0-1 multilinear programming as a unifying theory for LAD pattern generation , 2017, Discret. Appl. Math..

[6] Garth P. McCormick,et al. Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..

[7] J. Moon,et al. On cliques in graphs , 1965 .

[8] Hong Seo Ryoo,et al. MILP approach to pattern generation in logical analysis of data , 2009, Discret. Appl. Math..

[9] Fred W. Glover,et al. Technical Note - Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program , 1974, Oper. Res..

[10] Nikolaos V. Sahinidis,et al. Analysis of Bounds for Multilinear Functions , 2001, J. Glob. Optim..

[11] Yves Crama. Concave extensions for nonlinear 0–1 maximization problems , 1993, Math. Program..

[12] Hong Seo Ryoo,et al. Strong valid inequalities for Boolean logical pattern generation , 2017, J. Glob. Optim..