Research On The Perturbation Solution Properties Of Second-order Cone Constrained Variation Inequality Problems

Variation inequality problems are widely used in many fields such as computer science,route planning,operations research,etc.Furthermore,second-order cone programming is also one of the research hot spots in the field of optimization,and the study of variation inequalities is not yet mature.This paper focuses on the first-order necessary condition and second-order sufficient condition of the second-order cone-constrained variation inequality(SOCCVI)problem,as well as some traits of its perturbed solution.In order to study the behavior of the solution,this paper needs to prove the non-singularity of the equivalence equation of KKT(Karush-Kuhn-Tucker)condition transformation of SOCCVI,and use the second-order sufficient condition defines by myself in the proof process.Chapter 1,the theoretical value and practical significance of the solution of the SOCCVI problem are briefly described,as well as the background current situation of the research.The main research contents of this paper are briefly and concisely explained.Chapter 2,the preliminary knowledge used in the paper research is summarized,and the definitions of the tangent cone,the normal cone,the critical cone and the projection are given.The KKT condition of SOCCVI problem is transformed into a system of equations.The KKT system of the perturbation solution of the SOCCVI problem,and the KKT mapping set S(p)and the mapping set x(p)of the perturbed KKT points are given when the x is a function of random variablesp.Chapter 3,the first-order necessity condition and the second-order sufficient condition defined by itself are given.SOCCVI problem is transformed into a system of equations by the Natural Residual(NR)complementary function,and proved the nonsingularity of the operators of the KKT equations of the SOCCVI problem.Chapter 4,when the optimal solution x is a function about p,in order to further study the Lipschitz continuity of the perturbation solution of the SOCCVI problem,converting the perturbation solution problem of the KKT equations into the problem of solving the graph derivative.Chapter 5,Through the nature of the derivative of the graph,the main content of this paper is proved.The local lipschitz property of the perturbed KKT map set S(p)and the KKT point map set x(p)in terms of second-order sufficient conditions and strong constraints is local Lipschitz.Chapter 6,it provides a concise summary of the paper and looks forward to future issues such as SOCCVI.