Outer approximation algorithms for DC programs and beyond

This paper is a summary of the author’s Ph.D. thesis in Mathematics supervised by Giancarlo Bigi and Antonio Frangioni, and defended on 23 June 2008 at the Università di Pisa. The thesis is written in English and available from http://www.di.unipi.it/di/groups/optimize . The work deals with outer ap...

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Published in:4OR Vol. 8; no. 3; pp. 323 - 326
Main Author: Zhang, Qinghua
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.10.2010
Springer Nature B.V
Subjects:
Algorithms
Approximation
Business and Management
Convex analysis
Hierarchies
Industrial and Production Engineering
Mathematical analysis
Operations research
Operations Research/Decision Theory
Optimization
PhD Thesis
90C31
90C46
Approximation algorithms
Reverse polar constraint
90C26
Approximate optimality condition
DC program
Approximate oracle
ISSN:1619-4500, 1614-2411
Online Access:Get full text
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Summary:This paper is a summary of the author’s Ph.D. thesis in Mathematics supervised by Giancarlo Bigi and Antonio Frangioni, and defended on 23 June 2008 at the Università di Pisa. The thesis is written in English and available from http://www.di.unipi.it/di/groups/optimize . The work deals with outer approximation algorithms for solving an alternative equivalent formulation and a novel generalization of canonical DC (difference of convex) programs. The thesis develops an in-depth investigation of structural properties of both problems, and of the impact of approximations onto the quality of approximate optimal solutions. It also propose hierarchies of conditions guaranteeing convergence and develops several different implementable algorithms for canonical DC programs and its novel generalization, respectively.
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ISSN:1619-4500
1614-2411
DOI:10.1007/s10288-010-0126-8