An Efficient Neurodynamic Scheme for Solving a Class of Nonconvex Nonlinear Optimization Problems

Subject Areas : International Journal of Mathematical Modelling & Computations

Mohammad Moghaddas ¹ , Ghasem Tohidi ²

1 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

Received: 2018-10-09 Accepted : 2019-01-20 Published : 2018-11-01

Keywords: Neural network, ‎Nonconvex optimization, ‎p-power convexification method, ‎NCP function, ‎Lagrangian function,

Abstract :

‎By p-power (or partial p-power) transformation‎, ‎the Lagrangian function in nonconvex optimization problem becomes locally convex‎. ‎In this paper‎, ‎we present a neural network based on an NCP function for solving the nonconvex optimization problem‎. An important feature of this neural network is the one-to-one correspondence between its equilibria and KKT points of the nonconvex optimization problem. the proposed neural network is proved to be stable and convergent to an optimal solution of the original problem‎. ‎Finally‎, an ‎examples is provided to show the applicability of the proposed neural network‎.