| The eigenvalue complementarity problem is very important in optimization problems,which involves many fields in mathematics,physics and engineering,and solving the eigenvalue complementarity problem can effectively solve practical problems and has research significance.The study of the eigenvalue complementarity problem mainly consists of theoretical and algorithmic research.The Huber function is a combination of a quadratic function and an absolute value function,and it is smooth at the intersection.At the same time,it is more tolerant to noise and can better suppress the influence of outliers on the calculation results.The eigenvalue complementarity problem can be solved by transforming the NCP function into a nonlinear system of equations.In recent years,various methods for solving nonlinear systems of equations have been proposed one after another.Among these algorithms,Newton algorithm stands out because it is self-correcting,does not accumulate errors and has the greatest advantage of fast convergence.However,each iteration of Newton algorithm requires the computation of the Jacobian matrix and the selection of the initial point is also relatively strict.In order to solve the singularity of Jacobian matrix and meet the requirement of faster convergence,many improved Newton algorithms have been proposed.For example,the Newton-like algorithm,which does not need to compute the Jacobian matrix obviously,and maintains the faster convergence speed of Newton algorithm.The min function in the traditional NCP function is non-integrable at all points on this line of a(28)b,and the presence of its derivatives is required for solving the nonlinear system of equations using Newton algorithm.Therefore,a new Huber function based on the NCP function is constructed in this paper,and give a Newton algorithm and a Newton-like algorithm for solving the eigenvalue complementarity problem,and verify the effectiveness of these two algorithms by numerical examples. |
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