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Guaranteed accuracy for conic programming problems in vector lattices
Publikationstyp
Journal Article
Date Issued
2007-07-30
Sprache
English
Author(s)
Institut
TORE-URI
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex cones defining the partial ordering are not required to be polyhedral. In the case of linear programming, second order cone programming, and semidefinite programming specialized formulas are deduced yielding guaranteed accuracy. All computed bounds are completely rigorous because all rounding errors due to floating point arithmetic are taken into account. Numerical results, applications and software for linear and semidefinite programming problems are described.
Subjects
Linear programming
semidefinite programming
conic programming
convex programming
combinatorial optimization
rounding errors
ill-posed problems
interval arithmetic
branch-bound-and-cut
DDC Class
004: Informatik
510: Mathematik