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Afrika Matematika

, Volume 28, Issue 3–4, pp 333–356 | Cite as

Stable equilibrium configuration of two bar truss by an efficient nonmonotone global Barzilai–Borwein gradient method in a fuzzy environment

  • Hadi Nosratipour
  • Omid Solaymani Fard
  • Akbar Hashemi Borzabadi
  • Farhad Sarani
Article

Abstract

The stable equilibrium configuration of structures is a main goal in structural optimization. This goal may be achieved through minimizing the potential energy function. In the real world, sometimes, the input data and parameters of structural engineering design problems may be considered as fuzzy numbers which lead us to develop structural optimization methods in a fuzzy environment. In this regard, the present paper is intended to propose a fuzzy optimization scheme according to the nonmonotone globalization technique, the Barzilai–Borwein (BB) gradient method and the generalized Hukuhara differentiability (gH-differentiability). In fact, using the best benefits of BB-like methods i.e., simplicity, efficiency and low memory requirements, a modified global Barzilai–Borwein (GBB) gradient method is proposed for obtaining a non-dominated solution of the unconstrained fuzzy optimization related to the two bar asymmetric shallow truss in a fuzzy environment. The global convergence to first-order stationary points is also proved and the R-linear convergence rate is established under suitable assumptions. Furthermore, some numerical examples are given to illustrate the main results.

Keywords

Unconstrained fuzzy optimization Truss Generalized Hukuhara differentiability Nonmonotone line search Barzilai–Borwein gradient method 

Mathematics Subject Classification

80M50 94D05 90C52 

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Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Hadi Nosratipour
    • 1
  • Omid Solaymani Fard
    • 1
  • Akbar Hashemi Borzabadi
    • 1
  • Farhad Sarani
    • 1
  1. 1.Department of Applied Mathematics, School of Mathematics and Computer ScienceUniversity of DamghanDamghanIran

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