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A new trust region method for solving least-square transformation of system of equalities and inequalities

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Abstract

In this paper, a new nonmonotone trust region method with adaptive radius is proposed for solving system of equalities and inequalities. This method combines a new nonmonotone technique with a new adaptive strategy based on the Shi and Guo’s adaptive technique in (J Comput Appl Math 213:509–520, 2008), which makes full use of the current point information. Under some standard assumptions, the global convergence property as well as the superlinear convergence rate are established for the new method. Numerical results on some nonlinear systems of equalities and inequalities indicate the efficiency and robustness of the proposed method in practice.

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Acknowledgments

The authors would like to thank the Research Councils of K.N.Toosi University of Technology and Shahid Rajaee, Teacher Training University for supporting this research.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Shahid Rajaee, Teacher Training University, Tehran, Iran

    D. Ataee Tarzanagh & H. Mesgarani

  2. Department of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

    Z. Saeidian & M. Reza Peyghami

  3. Scientific Computations in Optimization and Systems Engineering (SCOPE), K.N. Toosi University of Technology, Tehran, Iran

    Z. Saeidian & M. Reza Peyghami

Authors
  1. D. Ataee Tarzanagh
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  2. Z. Saeidian
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  3. M. Reza Peyghami
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  4. H. Mesgarani
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Correspondence to M. Reza Peyghami.

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Tarzanagh, D.A., Saeidian, Z., Peyghami, M.R. et al. A new trust region method for solving least-square transformation of system of equalities and inequalities. Optim Lett 9, 283–310 (2015). https://doi.org/10.1007/s11590-013-0711-9

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  • DOI: https://doi.org/10.1007/s11590-013-0711-9

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