An accelerated Sobolev gradient method for unconstrained optimization problems based on variable inner products

We propose an accelerated version of the classical gradient method for unconstrained optimization problems defined on a Sobolev space H with Hilbert structure. Motivated by empirical results available in the literature demonstrating improved convergence of Sobolev gradient methods with suitably chosen weights, we develop a rigorous and constructive approach allowing one to identify the optimal gradient g k = g ( λ k ) among gradients g ( λ ) …