A Fast Accelerated Bundle Level Method for Large Scale Convex Optimization

We present a fast accelerated prox-level (FAPL) method for large scale ball constrained and unconstrained convex optimization. It achieves optimal iteration complexity in theory, and reduces computation time and increases accuracy significantly in practice. This is accomplished by reducing the number of sub-problems involved in most existing bundle level type methods, and the novel algorithm to solve the sub-problem exactly. Our numerical results on solving large-scale least square problems and total variation based image reconstruction have shown great advantages of the FAPL methods over several state-of-the-art firstorder methods.