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

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 ≤...

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Vydané v:Mathematical programming Ročník 136; číslo 1; s. 155 - 182
Hlavní autori: Misener, Ruth, Floudas, Christodoulos A.
Médium: Journal Article Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer-Verlag 01.12.2012
Springer
Springer Nature B.V
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Calculus of Variations and Optimal Control; Optimization
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ISSN:0025-5610, 1436-4646
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Popis
Shrnutí: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 ).
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-012-0555-6