DOI: http://dx.doi.org/10.18273/revint.v34n2-2016005

Un modelo de redes neuronales para
complementariedad no lineal

FAVIÁN ARENAS^*, ROSANA PÉREZ, HEVERT VIVAS

Universidad del Cauca, Departamento de Matemáticas, Popayán, Colombia.

Resumen. 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.

Palabras clave: Red neuronal, problema de complementariedad no lineal, estabilidad, reformulación.
MSC2010: 90C30, 90C33, 90C53, 90B10.

A neural network model for nonlinear
complementarity problems

Abstract. 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 functions. We establish the existence and convergence of the trajectory of the neural network, and we study its Lyapunov stability, asymptoticstability as well as exponential stability. Numerical tests verify the obtained theoretical results.

Keywords: Neural network, nonlinear complementarity problem, stability, reformulation.

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^*E-mail: farenas@unicauca.edu.co.
Recibido: 22 de junio de 2016, Aceptado: 21 de noviembre de 2016.
Para citar este artículo: F. Arenas, R. Pérez, H. Vivas, Un modelo de redes neuronales para complementa-
riedad no lineal, Rev. Integr. Temas Mat. 34 (2016), No. 2, 169-185.