SDPHA: A MATLAB implementation of homogeneous interior-point algorithms for semidefinite programming

Florian A. Potra, Rongqin Sheng, and Nathan Brixius

We implement Merhotra type primal-dual predictor-corrector interior-point algorithms for semidefinite programming by using the homogeneous formulation proposed and analyzed by Potra and Sheng. Three different search directions -- the AHO direction, the HKM direction, and the NT direction, are used. A rank-2 update technique is employed in our MATLAB code so that the computation of homogeneous directions is only slightly more expensive than in the non-homogeneous case. However, the homogeneous algorithms generally take fewer iterations to compute an approximate solution within a desired accuracy. Numerical results show that the homogeneous algorithms outperform their non-homogeneous counterparts, with improvement of more than $20\%$ in many cases, in terms of total CPU time.

REPORTS ON COMPUTATIONAL MATHEMATICS, NO. 100/1997, DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF IOWA, April, 1997

Contact: rsheng@math.uiowa.edu


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