Relaxations of Multilinear Convex Envelopes: Dual Is Better Than Primal [chapter]

Alberto Costa, Leo Liberti
2012 Lecture Notes in Computer Science  
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
more » ... se. We show that the natural relaxation obtained using duality performs more efficiently than the traditional method.
doi:10.1007/978-3-642-30850-5_9 fatcat:2acrmdbcrjanbjbbhjmmogzsc4