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Robert M. Freund (rfreundmit.edu) Abstract: We study four measures of problem instance behavior that might account for the observed differences in interiorpoint 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 nearabsence 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 nearabsence 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. Keywords: Semidefinite programming, behavioral measures, interiorpoint method Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: USCISE Technical Report #200502, University of Southern California, Los Angeles, CA 90089, February 2005. Download: [PDF] Entry Submitted: 02/28/2005 Modify/Update this entry  
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