Abstract: Recently, researchers proposed many accelerated project gradient methods based on new step length choice rules for large scale optimization problems. In this paper, we propose two project gradient methods with variants of new selection rules for quadratic programming with linear equality constraints. One is a non-monotone project gradient method for which an adaptive line search method is adopted and the Barzilai-Borwein step size is applied, and the other is a monotoneproject gradient method with Yuan step size. We give the global convergence of these two methods under mild assumptions. Numerical experiments indicate that both the new methods are more efficient than traditional project gradient methods.

Key words: Barzilai-Borwein step size, linear equality, project gradient