Combined bound-grid-factor constraints for enhancing RLT relaxations for polynomial programs

This paper studies the global optimization of polynomial programming problems using Reformulation-Linearization Technique (RLT)-based linear programming (LP) relaxations. We introduce a new class of bound-grid-factor constraints that can be judiciously used to augment the basic RLT relaxations in or...

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Bibliographic Details
Published in:Journal of global optimization Vol. 51; no. 3; pp. 377 - 393
Main Authors: Sherali, Hanif D., Dalkiran, Evrim
Format: Journal Article
Language:English
Published: Boston Springer US 01.11.2011
Springer Nature B.V
Subjects:
Computer Science
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Variables
Grid-factor constraints
Polynomial programs
BARON
Global optimization
Reformulation-linearization technique (RLT)
Cutting planes
Factorable programs
Valid inequalities
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:This paper studies the global optimization of polynomial programming problems using Reformulation-Linearization Technique (RLT)-based linear programming (LP) relaxations. We introduce a new class of bound-grid-factor constraints that can be judiciously used to augment the basic RLT relaxations in order to improve the quality of lower bounds and enhance the performance of global branch-and-bound algorithms. Certain theoretical properties are established that shed light on the effect of these valid inequalities in driving the discrepancies between RLT variables and their associated nonlinear products to zero. To preserve computational expediency while promoting efficiency, we propose certain concurrent and sequential cut generation routines and various grid-factor selection rules. The results indicate a significant tightening of lower bounds, which yields an overall reduction in computational effort for solving a test-bed of polynomial programming problems to global optimality in comparison with the basic RLT procedure as well as the commercial software BARON.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-010-9639-0