Abstract
A projection neural network method for circular cone programming is proposed. In the KKT condition for the circular cone programming, the complementary slack equation is transformed into an equivalent projection equation. The energy function is constructed by the distance function and the dynamic differential equation is given by the descent direction of the energy function. Since the projection on the circular cone is simple and costs less computation time, the proposed neural network requires less state variables and leads to low complexity. We prove that the proposed neural network is stable in the sense of Lyapunov and globally convergent. The simulation experiments show our method is efficient and effective.
Highlights
The circular cone is a pointed, closed, convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation [1,2,3]
We focus on neural network approach to the circular cone programming problem
The energy function is constructed by the distance function based on a cone projection function, whose solutions correspond to the KKT points of the circular cone programming
Summary
The circular cone is a pointed, closed, convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation [1,2,3]. Two types of neural networks are developed for the second-order cone programming and have shown some computational advantages. In paper [18], professor He proposed a neural network based on the simple projection and contraction technique for linear asymmetric variational inequalities. Inspired by the ideal projection and contraction technique and the new results about the projection conclusions on the circular cone [2], we can develop the projection neural network for the linear circular cone programming. We focus on neural network approach to the circular cone programming problem. We test the projection neural network by some numerical examples and the optimal grasping manipulation problems for multifingered robots and compare the neural network with the second neural network for some secondorder cone programming problems in paper [14].
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