An Optimal Subgradient Algorithm with Subspace Search for Costly Convex Optimization Problems

This paper presents an acceleration of the optimal subgradient algorithm OSGA (Neumaier in Math Program 158(1–2):1–21, 2016) for solving structured convex optimization problems, where the objective function involves costly affine and cheap nonlinear terms. We combine OSGA with a multidimensional subspace search technique, which leads to a low-dimensional auxiliary problem that can be solved efficiently. Numerical results concerning some applications are reported. A software package implementing the new method is available.