REMARKS ON THE GRADIENT-PROJECTION ALGORITHM - Su, M.; Xu, H. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
The gradient-projection algorithm (GPA) is a powerful method for solving constrained minimization problems infinite (and even infinite) dimensional Hilbert spaces. We consider GPA with variable stepsizes and show that if GPA generates a bounded sequence, then under certain assumptions, every accumulation point of the sequence is a solution of the minimization problem. We also look into the issue where the sequence of step sizes is allowed to be the limiting case (e.g., approaching to zero).