Mathematical Programming

, Volume 159, Issue 1–2, pp 339–369 | Cite as

Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem

  • Gabriel A. CarrizoEmail author
  • Pablo A. Lotito
  • María C. Maciel
Full Length Paper Series A


A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602–626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assumptions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical experience reported.


Multiobjective optimization Trust region Newton method Convergence 

Mathematics Subject Classification

90C29 65K05 49M37 



The authors are grateful to the anonymous reviewers, whose comments improved this work.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2015

Authors and Affiliations

  • Gabriel A. Carrizo
    • 1
    Email author
  • Pablo A. Lotito
    • 2
  • María C. Maciel
    • 1
  1. 1.Departamento de MatemáticaUniversidad Nacional del SurBahía BlancaArgentina
  2. 2.Universidad Nacional del CentroTandilArgentina

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