An interior point method for linearly constrained multiobjective optimization based on suitable descent directions

Enrico Miglierina, Elena Molho, Maria Cristina Recchioni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The aim of this paper is the development of an algorithm to find the critical points of a linearly constrained multiobjective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of projected gradient-like directions for the vector objective function. The method does not rely on an "a priori" scalarization of the vector objective function and is based on a dynamic system defined by a vector field of descent directions in the feasible region. We prove that the limit points of the solutions of the system satisfy the Karush-Kuhn-Tucker (KKT) first order necessary condition for the linearly constrained multiobjective optimization problem. The algorithm has been tested on some linearly constrained optimization problems and the numerical results obtained show that the algorithm approximates satisfactory the whole (weakly) local optimal Pareto set.
Original languageEnglish
Title of host publicationRecent Developments on Mathematical Programming and Applications
Pages89-102
Number of pages14
Publication statusPublished - 2009
EventWorkshop on Recent Developments on Mathematical Programming and Applications - Pisa
Duration: 5 Jun 20095 Jun 2009

Workshop

WorkshopWorkshop on Recent Developments on Mathematical Programming and Applications
CityPisa
Period5/6/095/6/09

Keywords

  • descent directions
  • gradient-like method
  • interior point method
  • multiple objective programming

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