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A neurodynamic optimization technique based on overestimator and underestimator functions for solving a class of non-convex optimization problems

Author

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  • Hosseinipour-Mahani, N.
  • Malek, A.

Abstract

In this paper, a novel neural network model for solving non-convex quadratic optimization problem is proposed. It is proved that the equilibrium points of the neural network model coincides with the local and global optimal solutions of the constrained non-convex optimization problem. Furthermore, it is shown that under suitable assumptions this model is globally convergent and stable in the sense of Lyapunov at each equilibrium points. Moreover a sufficient global optimality for non-convex non-quadratic objective function subject to a quadratic constraint is presented based on the corresponding underestimator function. Then for solving a class of non-convex optimization problems a novel neurodynamic optimization technique based on the necessary and sufficient global optimality is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for several different non-convex quadratic optimization problems are discussed to illustrate great agreement between the theoretical and numerical results. The efficiency of the proposed neural network model is illustrated by numerical simulations and comparisons with available literature models.

Suggested Citation

  • Hosseinipour-Mahani, N. & Malek, A., 2016. "A neurodynamic optimization technique based on overestimator and underestimator functions for solving a class of non-convex optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 20-34.
    • Handle: RePEc:eee:matcom:v:122:y:2016:i:c:p:20-34
    DOI: 10.1016/j.matcom.2015.09.013
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    References listed on IDEAS

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    1. Yi, Chenfu & Zhang, Yunong & Guo, Dongsheng, 2013. "A new type of recurrent neural networks for real-time solution of Lyapunov equation with time-varying coefficient matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 40-52.
    2. Yang, Yongqing & Cao, Jinde & Xu, Xianyun & Hu, Manfeng & Gao, Yun, 2014. "A new neural network for solving quadratic programming problems with equality and inequality constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 103-112.
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