Error Bounds For Linear Complementarity Problems For P-matrices

The linear complementarity problem(LCP(M,q))is an important class of optimization problems,which has a wide range of applications in many fields.The matrix M is a P-matrix(all its principal minors are positive)if and only if the LCP(M,q)has a unique solution.In the process of constructing the linear complementary problem model,the solutions obtained by different algorithms will have certain errors,so it is very important to find a sharper bound of the P-matrix linear complementarity problem.Based on the previous conclusions,the error bounds in the linear com-plementarity problem of B-matrix and BS-matrix are further reduced,and the error bound of the linear complementarity problem of Dashnic-Zusmanovich+matrix is obtained according to the related concepts and properties of the three subclasses(B-matrix,BS-matrix and Dashnic-Zusmanovich+ matrix)of P-matrix.This paper is divided into three parts.The first part studied the error bound of the B-matric linear complemen-tarity problem.By introducing the diagonal matrices ? and ? in linear comple-mentarity problems,combined the inequality of the scaling technique,the error bound of the original B-matrix linear complementarity problem is generalized,and get more accurate results.The second part studied the error bound of the BS-matric linear comple-mentarity problem.Construct a new M-matrix from the matrix element using the definition of BS-matrix.Combined with the scaling technique of inequal-ity,the new error bound of the linear complementarity problem of the special matrix is obtained.The third part studied the error bound of the Dashnic-Zusmanovich+matric linear complementarity problem.Constructing a monotonic function based on the estimator on upper bounds for the infinity norms of inverses of Dashnic-Zusmanovich+matric,and the error bound of the linear comple-mentarity problem of the matrix is obtained.