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A Capable Neural Network Framework for Solving Degenerate Quadratic Optimization Problems with an Application in Image Fusion

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Abstract

This paper presents a dynamic optimization scheme for solving degenerate convex quadratic programming (DCQP) problems. According to the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, a neural network model based on a dynamic system model is constructed. The equilibrium point of the model is proved to be equivalent to the optimal solution of the DCQP problem. It is also shown that the network model is stable in the Lyapunov sense and it is globally convergent to an exact optimal solution of the original problem. Several practical examples are provided to show the feasibility and the efficiency of the method.

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Acknowledgements

This work was supported by a research grant (ID: 23081) of Shahrood University of Technology.

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Authors and Affiliations

  1. Department of Mathematics, School of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran

    Alireza Nazemi

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  1. Alireza Nazemi
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Correspondence to Alireza Nazemi.

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Nazemi, A. A Capable Neural Network Framework for Solving Degenerate Quadratic Optimization Problems with an Application in Image Fusion. Neural Process Lett 47, 167–192 (2018). https://doi.org/10.1007/s11063-017-9640-4

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  • DOI: https://doi.org/10.1007/s11063-017-9640-4

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