Two Kinds Of Methods For Solving Double Obstacle Problems

In this paper,two methods are proposed to solve a nonlinear double obstacle complementa.rity problem.The first one is directly solving the double obstacle prob-lem.First,the nonlinear double obstacle complementarity problem is reformulated as a variational inequality problem,and then,the exist and uniqueness of the solu-tion for the double obst,acle variational inequality are proved under some suppositive conditions.Finally,a new penalty equation is defined by adding a new penalty ter-m,the existence and uniqueness of the solution for the function are also proved.We obtain a convergence rate that is corresponding to the power used in the formulation of the penalized equation.The second one is a method of the single obstacle problem approximate.First,the nonlinear double obstacle complementarity problem is refor-mulated as single obstacle variational inequality problem,the exist and uniqueness of the solution of single obstacle variational inequality are proved under some weak-er assumptions.By using the current penalty method for solving the single obstacle variational inequality problem,the approximate solution of the variational incquality problem is obtained,and then the solution of the nonlinear double obstacle comple-mentarity problem is obtained.At last.we demonstrate the effectiveness of the two methods through numerical calculations and compare the convergence rates.