Research On The Projection And Contraction Method For Two Types Of Cone Complementarity And Variation Inequality Problems

In recent years,optimization problems with cone structures have been extensively studied.And it has a wide range of applications in computer science and engineering issues.In addition,the second order cone is also one of the current research hot spots in the field of optimization.The research on circular cone and p-order cone is still very preliminary.This paper mainly uses the projection and contraction method to solve the complementarity and variational inequality problems of two cones.The main content of the paper is summarized as follows:The first chapter introduces the research background of the problem and related research progress at home and abroad,and describes the theoretical value and practical significance of the research,finally,the main research ideas of this article are explained concisely.The second chapter summarizes the preliminary knowledge which will be used in the research of the paper,and gives the definition and properties of circular cone,p-order cone and projection,etc.,then introduces the projection and contraction method.The third chapter firstly studies the projection and contraction method for the circular cone complementarity problem,then uses the complementary function to transform the circular cone complementarity problem into an unconstrained minimization problem,and uses the method to solve CCCP and prove convergence,finally,we give numerical examples to verify the effectiveness of the algorithm.Secondly,we use the projection and contraction method to solve the circular cone constrained variational inequality problem,and use the relationship between the variational inequality problem and its projection equation to turn the problem into a problem of solving the zero point of the projection residual,then use the method to solve the CCCVI and prove convergence,finally,the numerical results show that the calculation time and the number of iterations are very small and relatively stable,so as to illustrate its effectiveness.The fourth chapter firstly uses the complementary function to transform the p-order cone complementarity problem into an unconstrained minimization problem.In order to solve the minimization problem,the projection and contraction method is used to solve the problem and prove the convergence,numerical examples are given and verified the effectiveness of the algorithm.Secondly,we use the projection and contraction method to solve the p-order cone constrained variational inequality problem,by transforming the problem into the problem of solving the zero point of the projection residual,we use the method to solve the POVI and prove convergence,finally,we give numerical examples to verify the effectiveness of the algorithm.