Minimizing a quadratic over a sphere

A new method, the sequential subspace method (SSM), is developed for the pr oblem of minimizing a quadratic over a sphere. In our scheme, the quadratic is minimized over a subspace which is adjusted in successive iterations to ensure convergence to an optimum. When a sequential quadratic programming iterate is included in the subspace, convergence is locally quadratic. Nume rical comparisons with other recent methods are given.