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On verified numerical computations in convex programming
Publikationstyp
Journal Article
Date Issued
2009-10
Sprache
English
Author(s)
Institut
TORE-URI
Volume
26
Issue
2/3
Start Page
337
End Page
363
Citation
Japan Journal of Industrial and Applied Mathematics 2/3 (26): 337-363 (2009)
Publisher DOI
Scopus ID
Publisher
Springer Nature
This survey contains recent developments for computing verified results of convex constrained optimization problems, with emphasis on applications. Especially, we consider the computation of verified error bounds for non-smooth convex conic optimization in the framework of functional analysis, for linear programming, and for semidefinite programming. A discussion of important problem transformations to special types of convex problems and convex relaxations is included. The latter are important for handling and for reliability issues in global robust and combinatorial optimization. Some remarks on numerical experiences, including also large-scale and ill-posed problems, and software for verified computations concludes this survey.
Subjects
Branch-bound-and-cut
Combinatorial optimization
Conic programming
Convex programming
Ill-posed problems
Interval arithmetic
Linear programming
Rounding errors
Semidefinite programming
DDC Class
004: Informatik
510: Mathematik