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Numerical evaluation of SBmethod. (English) Zbl 1030.90100

Summary: We report numerical results for SBmethod – a publically available implementation of the spectral bundle method – applied to the 7th DIMACS challenge test sets that are semidefinite relaxations of combinatorial optimization problems. The performance of the code is heavily influenced by parameters that control bundle update and eigenvalue computation. Unfortunately, no mathematically sound guidelines for setting them are known. Based on our experience with SBmethod, we propose heuristics for dynamically updating the parameters as well as a heuristc for improving the starting point. These are now the default settings of SBmethod Version \(1.1\). We compare their performance on the DIMACS instances to our previous best choices for Version 1.0. SBmethod Version 1.1 is also part of the independent DIMACS benchmark by H. Mittelmann. Based on these results we try to analyze strengths and weaknesses of our approach in comparison to other codes for large scale semidefinite programming.

MSC:

90C27 Combinatorial optimization
90C22 Semidefinite programming
90-04 Software, source code, etc. for problems pertaining to operations research and mathematical programming
90C59 Approximation methods and heuristics in mathematical programming

Software:

SBmethod
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