Hybrid limited memory gradient projection methods for box-constrained optimization problems

Abstract Gradient projection methods represent effective tools for solving large-scale constrained optimization problems thanks to their simple implementation and low computational cost per iteration. Despite these good properties, a slow convergence rate can affect gradient schemes, especially when high accurate solutions are needed. A strategy mitigate this drawback consists in properly selecting the values steplength along negative gradient. In paper, we consider class of with line search projected arc box-constrained minimization analyse different strategies define steplength. It is well known literature that selection rules able approximate, at each iteration, eigenvalues inverse suitable submatrix Hessian objective function improve performance methods. perspective, propose an automatic hybrid technique employs proper alternation standard Barzilai–Borwein rules, final active set not approximated, generalized limited memory based on Ritz-like matrix restricted inactive constraints, reached. Numerical experiments quadratic non-quadratic test show effectiveness proposed scheme.