Sensitivity Result and Convergence Analysis
for a Sequential Semidefinite Programming Method

Florian Jarre
Universitaet  Duesseldorf
Germany


We present a simple sensitivity result for solutions
of linear semidefinite programs under small arbitrary
perturbations of the data. The result is generalized
to nonlinear programs with nonlinear semidefiniteness
constraints.
This generalization is used to derive an elementary and
self-contained proof of local quadratic convergence of
a sequential semidefinite programming (SSP) method.

A key advantage of the SSP method lies in the fact
that the choice of the symmetrization procedure can
be shifted in a very natural way to the linear
semidefinite subproblems, and thus being separated
from the process of linearizing and convexifying the
data of the nonlinear SDP.
Globalization techniques and small scale numerical
results will be discussed.



This work is joint with Roland W. Freund
(Bell  Laboratories, Murray Hill, NJ, USA)