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|Abstract:||We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to 𝜖 -global optimality. The facets of low-dimensional (n ≤ 3) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge-concave aggregations are addressed through piecewise-linear relaxations. Extensive computational studies are presented for point packing problems, standard and generalized pooling problems, and examples from GLOBALLib (Meeraus, Globallib. http://www.gamsworld.org/global/globallib.htm).|
|Citation:||Misener, Ruth, and Christodoulos A. Floudas. "Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations." Mathematical Programming 136, no. 1 (2012): 155-182. doi: 10.1007/s10107-012-0555-6|
|Pages:||155 - 182|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Mathematical Programming|
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