A Convex Envelope Formula for Multilinear Functions
Journal of Global Optimization
Pooling Problem: Alternate Formulations and Solution Methods
Management Science
Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes
Journal of Global Optimization
Studies of the behavior of recursion for the pooling problem
ACM SIGMAP Bulletin
Reformulation in mathematical programming: An application to quantum chemistry
Discrete Applied Mathematics
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
Branching and bounds tighteningtechniques for non-convex MINLP
Optimization Methods & Software - GLOBAL OPTIMIZATION
On convex relaxations of quadrilinear terms
Journal of Global Optimization
Static Analysis by Abstract Interpretation: A Mathematical Programming Approach
Electronic Notes in Theoretical Computer Science (ENTCS)
Valid inequalities for the pooling problem with binary variables
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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Bilinear, trilinear, quadrilinear and general multilinear terms arise naturally in several important applications and yield nonconvex mathematical programs, which are customarily solved using the spatial Branch-and-Bound algorithm. This requires a convex relaxation of the original problem, obtained by replacing each multilinear term by appropriately tight convex relaxations. Convex envelopes are known explicitly for the bilinear case, the trilinear case, and some instances of the quadrilinear case. We show that the natural relaxation obtained using duality performs more efficiently than the traditional method.