Parameterized eigensolution technique for solving constrained least squares problems

This paper aims to introduce an algorithm for solving large scale least squares problems subject to quadratic inequality constraints. The algorithm recasts the least squares problem in terms of a parameterized eigenproblem. A variant of k-step Arnoldi method is determined to be well suited for computing the parameterized eigenpair. A two-point interpolating scheme is developed for updating the parameter. A local convergence theory for this algorithm is presented. It is shown that this algorithm is superlinearly convergent.