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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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
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ISSN	0025-5610 1436-4646
DOI	10.1007/s10107-012-0555-6

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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 -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 ).
AbstractList	(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Issue Title: Special Issue on Parametric Optimization - Recent Advances 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).[PUBLICATION 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 $${\epsilon}$$ -global optimality. The facets of low-dimensional (n less than or equal to 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). 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 ).
Author	Floudas, Christodoulos A. Misener, Ruth
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Title	Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations
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