Solving linear vector optimization problems with the Alternating Direction Method of Multipliers

Speaker

Daniel Hernandez Escobar

Abstract

We consider the numerical solution of optimization problems with vector-valued objectives, where preferences are encoded by a generalized inequality rather than the usual componentwise order. We focus on the linear case and propose a highly parallelizable solution strategy based on the Alternating Direction Method of Multipliers (ADMM). The proposed method can exploit GPUs or TPUs to achieve fast convergence to accuracy levels that are typically sufficient in practice. It is also sufficiently robust to support extensions such as Pareto navigation and alternative warm-start strategies. We illustrate the approach on problems in which the generalized inequality is induced by the Lorentz cone.