Outer approximation algorithms for canonical DC problems

The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditio...

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Bibliographic Details
Published in:Journal of global optimization Vol. 46; no. 2; pp. 163 - 189
Main Authors: Bigi, Giancarlo, Frangioni, Antonio, Zhang, Qinghua
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2010
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computer Science
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Polar set
Cutting plane algorithms
DC problems
Approximate optimality conditions
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditions are introduced and bounds on the quality of the approximate global optimal solution are obtained. A thorough analysis of properties which guarantee convergence is carried out; two families of conditions are introduced which lead to design six implementable algorithms, whose convergence can be proved within a unified framework.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-009-9415-1