An Optimal Algorithm for Bound and Equality Constrained Quadratic Programming Problems with Bounded Spectrum

An implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for solving the large convex bound and equality constrained quadratic programming problems is considered. It is proved that if the algorithm is applied to the class of problems with uniformly bounded spectrum of the Hessian matrix, then the algorithm finds an approximate solution at O(1) matrix-vector multiplications. The optimality results are presented that do not depend on conditioning of the matrix which defines the equality constraints. Theory covers also the problems with dependent constraints. Theoretical results are illustrated by numerical experiments.