An extended projected residual algorithm for solving smooth convex optimization problems

Abstract

A projected residual algorithm for solving smooth convex optimization problems is presented. The proposed method is an extension of a residual algorithm for solving systems of nonlinear monotone equations introduced by La Cruz (2017), which uses in a systematic way the residual as a search direction combined with the Barzilai–Borwein’s choice of the step size and a line search globalization strategy that does not impose the condition that the function value to decrease monotonically at every iteration. The global and R-sublinear convergence of the new method is established. With the aim of showing the advantages of the proposed global scheme an extensive set of numerical experiments including standard test problems and some specific applications are reported.