A proportioning based algorithm with rate of convergence for bound constrained quadratic programming

Abstract

The proportioning algorithm with projections turned out to be an efficient algorithm for iterative solution of large quadratic programming problems with simple bounds and box constraints. Important features of this active set based algorithm are the adaptive precision control in the solution of auxiliary linear problems and capability to add or remove many indices from the active set in one step. In this paper a modification of the algorithm is presented that enables to find its rate of convergence in terms of the spectral condition number of the Hessian matrix and avoid any backtracking. The modified algorithm is shown to preserve the finite termination property of the original algorithm for problems that are not dual degenerate.