eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2006-01-31
1
8
10.4230/DagSemProc.05391.7
article
Rigorous Results in Combinatorial Optimization
Jansson, Christian
Many current deterministic solvers for NP-hard
combinatorial optimization problems are based on nonlinear
relaxation techniques that use floating point arithmetic.
Occasionally, due to solving these relaxations, rounding errors
may produce erroneous results, although the deterministic
algorithm should compute the exact solution in a finite number of
steps. This may occur especially if the relaxations are
ill-conditioned or ill-posed, and if Slater's constraint
qualifications fail. We show how exact solutions can be obtained
by rigorously bounding the optimal value of semidefinite
relaxations, even in the ill-posed case. All rounding errors due
to floating point arithmetic are taken into account.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05391/DagSemProc.05391.7/DagSemProc.05391.7.pdf
Combinatorial Optimization
Semidefinite Programming
Ill-posed Problems
Verification Methods