Japan Journal of Industrial and Applied Mathematics

On Verified Numerical Computations in Convex Programming

Christian Jansson

Full-text: Open access

Abstract

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.

Article information

Source
Japan J. Indust. Appl. Math., Volume 26, Number 2-3 (2009), 337-363.

Dates
First available in Project Euclid: 1 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.jjiam/1265033786

Mathematical Reviews number (MathSciNet)
MR2589480

Zentralblatt MATH identifier
1184.90124

Keywords
linear programming semidefinite programming conic programming convex programming combinatorial optimization rounding errors ill-posed problems interval arithmetic branch-bound-and-cut

Citation

Jansson, Christian. On Verified Numerical Computations in Convex Programming. Japan J. Indust. Appl. Math. 26 (2009), no. 2-3, 337--363. https://projecteuclid.org/euclid.jjiam/1265033786


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