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 epsilon-global optimality. The facets of low-dimensional (n < 4) 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 .
Mathematical Programming; 136 (1) pp. 155-182; 2012 (DOI 10.1007/s10107-012-0555-6)
View Global Optimization of Mixed-Integer Quadratically-Constrained Quadratic Programs (MIQCQP) through Piecewise-Linear and Edge-Concave Relaxations