RANDOMLY GENERATED TEST PROBLEMS FOR POSITIVE DEFINITE QUADRATIC-PROGRAMMING

A procedure is described for randomly generating positive definite quadratic programming test problems. The test problems are constructed in the form of linear least-squares problems subject to linear constraints. The probability measure for the problems so generated is invariant under orthogonal transformations. The procedure allows the user to specify the size of the least-squares problem (number of unknown parameters, number of observations, and number of constraints), the relative magnitude of the residuals, the condition number of the Hessian matrix of the objective function, and the structure of the feasible region (the number of equality constraints and of inequalities which will be active at the feasible starting point and at the optimal solution). An example is given illustrating how these problems can be used to evaluate the performance of a software package.