Open Access
October 2009 On Verified Numerical Computations in Convex Programming
Christian Jansson
Japan J. Indust. Appl. Math. 26(2-3): 337-363 (October 2009).


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.


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Christian Jansson. "On Verified Numerical Computations in Convex Programming." Japan J. Indust. Appl. Math. 26 (2-3) 337 - 363, October 2009.


Published: October 2009
First available in Project Euclid: 1 February 2010

zbMATH: 1184.90124
MathSciNet: MR2589480

Keywords: branch-bound-and-cut , Combinatorial optimization , conic programming , Convex programming , Ill-posed problems , interval arithmetic , linear programming , rounding errors , semidefinite programming

Rights: Copyright © 2009 The Japan Society for Industrial and Applied Mathematics

Vol.26 • No. 2-3 • October 2009
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