Global optimization of general nonconvex problems with intermediate polynomial substructures

This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that...

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Vydáno v:Journal of global optimization Ročník 59; číslo 2-3; s. 673 - 693
Hlavní autoři: Zorn, Keith, Sahinidis, Nikolaos V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.07.2014
Springer
Springer Nature B.V
Témata:
Algorithms
Branch & bound algorithms
Computer Science
Cutting
Filtering
Linear programming
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Planes
Polynomials
Real Functions
Studies
Substructures
Variables
Factorable polyhedral relaxation
Reformulation-linearization techniques
Branch-and-bound global optimization
Polynomial programming
ISSN:0925-5001, 1573-2916
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Shrnutí:This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that exploit these underlying structures. These cutting plane strategies simultaneously convexify linear and nonlinear terms from multiple constraints and are highly effective at tightening standard linear programming relaxations generated by sequential factorable programming techniques. Because the number of available cutting planes increases exponentially with the number of variables, we implement cut filtering and selection strategies to prevent an exponential increase in relaxation size. We introduce algorithms for polynomial substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in BARON at every node in the branch-and-bound tree. A computational study including randomly generated problems of varying size and complexity demonstrates that the exploitation of underlying polynomial substructures significantly reduces computational time, branch-and-bound tree size, and required memory.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-014-0190-2