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Search directions for primal-dual interior point
methods in semidefinite programming

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K.C. Toh

Search directions for primal-dual path-following methods
for semidefinite programming are proposed.
These directions have the properties that
- under nondegeneracy
and strict complementarity assumptions, the Jacobian
matrix of the associated symmetrized Newton equation has bounded
condition number along the central path
in the limit as the barrier parameter $\mu$
tends to zero;
- the Schur complement matrix
of the symmetrized Newton equation is symmetric positive
definite if $\mu > 0$.

These two properties imply that a path-following method
using the proposed direction can achieve the high accuracy typically
attained by the AHO method, but each iteration requires at most
half the amount of flops, to leading orders.
Technical Report, Department of Mathematics,
National University of Singapore, Singapore,
July, 1997

Contact: mattohkc@math.nus.sg