On the experimental investigation of Pareto–Lipschitzian optimization

Abstract

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto Lipschitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitzconstants.In the proposed approach, a set of all unknown Lipschitz constants is regarded as multiple criteria using the concept of Pareto Optimality (PO).