Preconditioned Steepest Descent (PSD) solver for regularized convex optimization problems
摘要：A few preconditioned steepest descent (PSD) solvers are presented for the certain optimization problems, in which the solution corresponds to a convex energy functional. The highest and lowest order terms are constant-coefficient, positive linear operators. By using the energy dissipation property, we derive a discrete bound for the solution, as well as an upper-bound for the second derivative of the energy. These bounds allow us to investigate the convergence properties of our method. In particular, a geometric convergence rate is shown for the nonlinear PSD iteration applied to the regularized equation, which provides a much sharper theoretical result over the existing works. Some numerical simulation results are also presented in the talk.