A Kind of Stochastic Eigenvalue Complementarity Problems

Ying-Xiao Wang,Shou-Qiang Du

doi:10.1155/2018/7397592

Abstract

With the development of computer science, computational electromagnetics have also been widely used. Electromagnetic phenomena are closely related to eigenvalue problems. On the other hand, in order to solve the uncertainty of input data, the stochastic eigenvalue complementarity problem, which is a general formulation for the eigenvalue complementarity problem, has aroused interest in research. So, in this paper, we propose a new kind of stochastic eigenvalue complementarity problem. We reformulate the given stochastic eigenvalue complementarity problem as a system of nonsmooth equations with nonnegative constraints. Then, a projected smoothing Newton method is presented to solve it. The global and local convergence properties of the given method for solving the proposed stochastic eigenvalue complementarity problem are also given. Finally, the related numerical results show that the proposed method is efficient.

Highlights

Computational electromagnetics is a science, which spans many subjects
In this paper, we propose a new kind of stochastic eigenvalue complementarity problem and the smoothing Newton method is proposed to solve the given problem
The cavity is filled with air or other mediums, and the electromagnetic oscillation in the cavity can be generated in the cavity by the way of probe and small hole

Summary

Introduction

Computational electromagnetics is a science, which spans many subjects. It is an organic combination of mathematical theory, electromagnetic theory, and computer science. We consider establishing a new model to solve some related electromagnetics problems. This is the motivation of this paper. In [9], the eigenvalue complementarity problems with symmetric real matrices are considered The authors transform this problem into a differentiable optimization program involving the Rayleigh quotient on a simplex and find its stationary point by the spectral projected gradient algorithm. In order to reduce the difference between calculation and measurement in computational electromagnetics, we consider getting the approximate distribution, by statistics, of a large number of experimental data and establishing a new stochastic model. In this paper, we propose a new kind of stochastic eigenvalue complementarity problem and the smoothing Newton method is proposed to solve the given problem.

Preliminary Results

Projected Smoothing Newton Method and Convergence Analysis

Numerical Results

Conclusion