Extended reverse-convex programming: an approximate enumeration approach to global optimization

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many branch-and-bound methods, the proposed approach approximates the NL...

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Bibliographic Details
Published in:Journal of global optimization Vol. 65; no. 2; pp. 191 - 229
Main Author: Bunin, Gene A.
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2016
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Candidates
Computer Science
Enumeration
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Programming
Real Functions
Regularity
Strategy
Studies
Variables
Implicit enumeration methods
Concave programming
Factorable programming
Piecewise-concave approximation
Reverse-convex programming
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many branch-and-bound methods, the proposed approach approximates the NLP problem by a reverse-convex programming (RCP) problem to a controlled precision, with the latter then solved by an enumerative search. To establish the theoretical guarantees of the method, the notion of “RCP regularity” is introduced and it is proven that enumeration is guaranteed to yield a global optimum when the RCP problem is regular. An extended RCP algorithmic framework is then presented and its performance is examined for a small set of test problems.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-015-0352-x