Nonlinear Multi-Objective Constrained Optimization (in English)
Alexis Pospelov, Fedor Gubarev
20th Conference of the International Federation of Operational Research Societies, 2014
Local geometry of the Pareto front allows building efficient algorithms to discover the frontier. However, in many applications it’s not sufficient to use only linear approximations to optimal variety. In this work we propose to use second-order local approximation to the Pareto frontier. Within the descent-diffusion algorithm, presented in supplementary talk, our approach allows efficient discovery of Pareto frontier even in problems with singular Hessians, where linear approximations perform poorly because of large number of very small steps.