Florian Jarre
"A QQP-Minimization Method for Semidefinite and Smooth Nonconvex Programs"
In many applications, semidefinite programs with nonlinear equality
constraints arise. These problems are nonconvex, and the common
interior-point results no longer apply. We give two such examples
to emphasize the importance of this class of problems.
To solve such problems we propose an interior-point method in which
the usual linear systems of the Newton step and of the predictor step
are replaced by simple quadratically constrained quadratic programs.
These QQP's are of a special structure and can be solved directly.
In addition, the QQP's allow for a special line search which effects
that the algorithm is applicable to nonconvex programs.
Some convergence results are given, and some preliminary numerical
examples show the behaivour of the QQP-steps for nonconvex minimization.
helmberg@zib.de
Last Update: September 16, 1998