A variational approach to define robustness for parametric multiobjective optimization problems

  • Authors:

  • Katrin Witting;Sina Ober-Blöbaum;Michael Dellnitz

  • Affiliations:

  • Chair of Applied Mathematics, University of Paderborn, Paderborn, Germany 33098;Computational Dynamics and Optimal Control, University of Paderborn, Paderborn, Germany 33098;Chair of Applied Mathematics, University of Paderborn, Paderborn, Germany 33098

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter $${\lambda \in \mathbb{R}}$$ , so-called parametric multiobjective optimization problems. The solution of such a problem is given by the 驴-dependent Pareto set. In this work we give a new definition that allows to characterize 驴-robust Pareto points, meaning points which hardly vary under the variation of the parameter 驴. To describe this task mathematically, we make use of the classical calculus of variations. A system of differential algebraic equations will turn out to describe 驴-robust solutions. For the numerical solution of these equations concepts of the discrete calculus of variations are used. The new robustness concept is illustrated by numerical examples.