Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations

• Published in: Mathematical programming Vol. 136; no. 1; pp. 155 - 182
• Main Authors: Misener, Ruth, Floudas, Christodoulos A.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.12.2012; Springer; Springer Nature B.V
• Subjects: Agglomeration; Applied sciences; Batch processes; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Computation; Exact sciences and technology; Flows in networks. Combinatorial problems; Full Length Paper; Inventory control, production control. Distribution; Investigations; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Multivariable; Numerical Analysis; Operational research and scientific management; Operational research. Management science; Optimization; Optimization algorithms; Quadratic programming; Scholarships & fellowships; Studies; Theoretical; Trees; Variables; 90C20 Quadratic programming; 90C26 Global optimization; 90C57 Polyhedral combinatorics; branch & bound; Branching; Group technology; Non convex programming; Tree(graph); Program library; Branch and bound method; Global optimum; Bin packing problem; Mixed integer programming; Combinatorial optimization; Quadratic programming; Standards; Constrained optimization; Aggregation; Polyhedron; Integer programming; 90C20; Implicit enumeration method; Non convex analysis; Piecewise linearization; Mathematical programming; Piecewise-linear techniques
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-012-0555-6

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 -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 ).