Particle Swarm Optimization For Eigenvalue Complementarity Problem

The complementary problem of the characteristic value is the extension of the eigenvalue problem in the linear algebra,and it has close relation with many problems,such as the nonlinear complementarity problem,the differentiable optimization problem,the variational inequality,and so on.It has been widely used in engineering and physics,such as the study of mechanical contact problems,the dynamic analysis of structural mechanical systems and so on.Therefore,the study of eigenvalue complementarity problem has both theoretical significance and application value.Particle Swarm Optimization is a swarm intelligence algorithm,which from the study of foraging behavior of birds,the solution is searched by the particles that follow the optimal particles in the solution space.Particle swarm optimization algorithm has the advantages of simple algorithm,few parameters and easy implementation,so for many complex optimization problems,particle swarm optimization algorithm can use a simple way to get better results.In this paper,the eigenvalue complementarity problem is transformed into semi-smooth nonlinear system by Fischer-Burmeister(FB)function,and the basic particle swarm optimization algorithm and second-order particle swarm optimization algorithm for eigenvalue complementarity problem are given.The convergence of the algorithm is proved respectively,the effectiveness of the algorithm isverified by numerical examples.