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Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

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Show simple item record Freund, Robert M. Ordóñez, Fernando Toh, Kim Chuan 2005-03-04T19:58:06Z 2005-03-04T19:58:06Z 2005-03-04T19:58:06Z
dc.description.abstract We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations. en
dc.format.extent 288865 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.relation.ispartofseries Operations Research Center Working Paper Series;OR 374-05
dc.subject problem instance behavior en
dc.subject interior-point method en
dc.subject semidefinite programming en
dc.subject aggregate geometry en
dc.subject IPM en
dc.subject SDP en
dc.title Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems en
dc.type Working Paper en

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