 
Summary: 1
Hybrid Methods for Minimizing Least Distance Functions
with SemiDefinite Matrix Constraints
Suliman AlHomidan
Department of Mathematics, King Fahd University of Petroleum and Minerals,
Dhahran 31261, PO Box 119, Saudi Arabia
Abstract
Hybrid methods for minimizing least distance functions with semidefinite
matrix constraints are considered. One approach is to formulate the problem as
a constrained least distance problem in which the constraint is the intersection
of three convex sets. The DykstraHan projection algorithm can then be used
to solve the problem. This method is globally convergent but the rate of con
vergence is slow. However, the method does have the capability of determining
the correct rank of the solution matrix, and this can be done in relatively few
iterations. If the correct rank of the solution matrix is known, it is shown
how to formulate the problem as a smooth nonlinear minimization problem, for
which a rapid convergence can be obtained by l1SQP method. Also this paper
studies hybrid method that attempt to combine the best features of both types
of methods. An important feature concerns the interfacing of the component
methods. Thus, it has to be decided which method to use first, and when to
