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,