Un modelo de redes neuronales para complementariedad no lineal

• Arenas, Favián ^[1] ; Pérez, Rosana ^[1] ; Vivas, Hevert ^[1]
  1. [1] Universidad del Cauca

     Universidad del Cauca

     Colombia

     
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 34, Nº. 2, 2016 (Ejemplar dedicado a: Revista Integración), págs. 169-185
• Idioma: español
• DOI: 10.18273/revint.v34n2-2016005
• Títulos paralelos:
  • A neural network model for nonlinear complementarity problems
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• Resumen
  • español

    En este artículo presentamos un modelo de red neuronal para resolver el problema de complementariedad no lineal. Para ello, reformulamos este problema como uno de minimización sin restricciones usando una familia uniparamétrica de funciones de complementariedad. Demostramos resultados de existencia y convergencia de la trayectoria de la red neuronal, así como resultados de estabilidad en el sentido de Lyapunov, estabilidad asintótica y exponencial. Además, presentamos resultados numéricos preliminares que ilustran un buen desempeño práctico del modelo.

  • English

    In this paper we present a neural network model for solving the nonlinear complementarity problem. This model is derived from an equivalent unconstrained minimization reformulation of the complementarity problem, which is based on a one-parametric class of nonlinear complementarity func- tions. We establish the existence and convergence of the trajectory of the neural network, and we study its Lyapunov stability, asymptoti stabilityc as well as exponential stability. Numerical tests verify the obtained theoretical results.

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