A Newton-Like Method for Variable Order Vector Optimization Problems

  • Glaydston de Carvalho Bento
  • Gemayqzel Bouza Allende
  • Yuri Rafael Leite Pereira


A Newton approach is proposed for solving variable order smooth constrained vector optimization problems. The concept of strong convexity is presented, and its properties are analyzed. It is thus obtained that the Newton direction is well defined and that the algorithm converges. Moreover, the rate of convergence is obtained under ordering structures satisfying a mild hypothesis.


Descent direction Efficient points K-strong convexity Newton method Variable order vector optimization 

Mathematics Subject Classification

90C29 90C30 26B25 65K05 



The first author was partially supported by CNPq Grants 458479/2014-4 and 3122077/2014-9, the second author was partially supported by CAPES/FAPEG 10/2013 and 08/2014, and the third author was partially supported by CAPES, CAPES/MES/Cuba Project 226/2012 Optimization and Applications. The second author was also partially supported by Alexander von Humboldt Foundation during his stay at Martin Luther University, where part of this research was carried out.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Glaydston de Carvalho Bento
    • 1
  • Gemayqzel Bouza Allende
    • 2
  • Yuri Rafael Leite Pereira
    • 3
  1. 1.IMEUniversidade Federal de GoiásGoiâniaBrazil
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of HabanaHabanaCuba
  3. 3.DMUniversidade Federal do PiauíTeresinaBrazil

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