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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Veröffentlicht in:Mathematical programming Jg. 136; H. 1; S. 155 - 182
Hauptverfasser: Misener, Ruth, Floudas, Christodoulos A.
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 01.12.2012
Springer
Springer Nature B.V
Schlagworte:
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
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Beschreibung
Zusammenfassung: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