Hybrid methods for solving the educational testing problem

Methods for solving the educational testing problem are considered. One approach (Glunt 1995) is to formulate the problem as a linear convex programming problem in which the constraint is the intersection of three convex, sets. This method is globally convergent but the rate of convergence 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 [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 first, and when to switch between methods. Difficulties such as these are addressed in the paper. Comparative numerical results are also reported.