Techniques for Solving Bound-Constrained Convex Optimization Using Spectral Projected Conjugate Gradient Based on Barzilai-Borwein Step Length

This work aims to create an effective spectral conjugate gradient for non-linear optimization problems and to project the solution into a bounded convex set for largescale optimization problems. We do this by combining the classical spectral conjugated gradient direction with the projected Barzilai and Borwein step lengths. The efficacy and convergence of the new method are illustrated through a series of problems.