Mathematical Programming

, Volume 131, Issue 1–2, pp 131–161 | Cite as

Multicriteria optimization with a multiobjective golden section line search

  • Douglas A. G. Vieira
  • Ricardo H. C. TakahashiEmail author
  • Rodney R. Saldanha
Full Length Paper Series A


This work presents an algorithm for multiobjective optimization that is structured as: (i) a descent direction is calculated, within the cone of descent and feasible directions, and (ii) a multiobjective line search is conducted over such direction, with a new multiobjective golden section segment partitioning scheme that directly finds line-constrained efficient points that dominate the current one. This multiobjective line search procedure exploits the structure of the line-constrained efficient set, presenting a faster compression rate of the search segment than single-objective golden section line search. The proposed multiobjective optimization algorithm converges to points that satisfy the Kuhn-Tucker first-order necessary conditions for efficiency (the Pareto-critical points). Numerical results on two antenna design problems support the conclusion that the proposed method can solve robustly difficult nonlinear multiobjective problems defined in terms of computationally expensive black-box objective functions.


Multiobjective optimization Feasible directions Line search Golden section 

Mathematics Subject Classification (2000)

90C29 90C30 65K05 


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Copyright information

© Springer and Mathematical Programming Society 2010

Authors and Affiliations

  • Douglas A. G. Vieira
    • 1
  • Ricardo H. C. Takahashi
    • 2
    Email author
  • Rodney R. Saldanha
    • 1
  1. 1.Departamento de Engenharia ElétricaUniversidade Federal de Minas GeraisMinas GeraisBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal de Minas GeraisMinas GeraisBrazil

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