Neural networks for solving second-order cone constrained variational inequality problem

Abstract

In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-KuhnTucker (KKT) conditions of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) function to achieve an unconstrained minimization which is a merit function of the Karush-Kuhn-Tucker equation. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network is introduced for solving a projection formulation whose solutions coincide with the KKT triples of SOCCVI problem. Its Lyapunov stability and global convergence are proved under some conditions. Simulations are provided to show effectiveness of the proposed neural networks.

A practical nonlinear dynamic framework for solving a class of fractional programming problems

“…Moreover, from Theorem 4.1 we see that the equilibrium point of the proposed neural network model (40) and (41) satisfies the KKT system (36). Thus, the equilibrium point of the network (40) and (41) is unique.…”

Dynamic Model of a Wind Turbine for the Electric Energy Generation

“…The proposed dynamic model could be used on control, prediction, or classification. As a future research, the modeling will be improved using other interesting methods as the least squares in [16][17][18][19][20][21][22][23][24][25][26], neural networks in [14,[27][28][29][30][31][32], or fuzzy systems in [15,[33][34][35].…”

Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete‐Type Classes of SOC Complementarity Functions

“…where ( , , ) = ( ) + ∇ℎ( ) + ∇ ( ) is the variational inequality Lagrangian function, ∈ R and ∈ R . We also point out that the neural network approach for SOCCVI was already studied in [32]. Here we revisit the SOCCVI with different neural models.…”

“…Following the similar idea, researchers have also developed many continuous-time neural networks for secondorder cone constrained optimization problems. For example, Ko, Chen and Yang [31] proposed two kinds of neural networks with different SOCCP functions for solving the 2 Mathematical Problems in Engineering second-order cone program; Sun, Chen, and Ko [32] gave two kinds of neural networks (the first one is based on the Fischer-Burmeister function and the second one relies on a projection function) to solve the second-order cone constrained variational inequality (SOCCVI) problem; Miao, Chen, and Ko [33] proposed a neural network model for efficiently solving general nonlinear convex programs with second-order cone constraints. In this paper, we are interested in employing neural network approach for solving two types of SOC constrained problems, the quadratic programming problems with second-order cone constraints (SOCQP for short) and the second-order cone constrained variational inequality (SOCCVI for short), whose mathematical formats are described as below.…”