 
Summary: 1
Hybrid Methods for Solving the
Educational Testing Problem
Suliman AlHomidan
Department of Mathematics, King Fahd University of Petroleum and Minerals,
Dhahran 31261, PO Box 119, Saudi Arabia
Abstract
Methods for solving the educational testing problem are considered. One
approach (Glunt [7]) is to formulate the problem as a linear convex program
ming problem in which the constraint is the intersection of three convex sets.
This method is globally convergent but the rate of convergence is slow. How
ever, 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 l 1 SQP method [6]. This paper studies hybrid methods that
attempt to combine the best features of both types of method. An important
feature concerns the interfacing of the component methods. Thus, it has to
be decided which method to use rst, and when to switch between methods.
DiĘculties such as these are addressed in the paper. Comparative numerical
