| In this thesis,we mainly study nonlinear programming problem with switching constraints.Firstly,the dual relation between the mathematical program with switching constraint and the dual problem of Wolfe type and Mond-Weir type is studied.Secondly,the sequential quadratic programming method of mathematical program with switching constraint is studied.Firstly,the research background and significance of the mathematical program with switching constraint are described.And the research status of dual theory and sequential quadratic programming method is summarized and analyzed.Then the research motivation and the main research content of this thesis are introduced.Then,the following contents are listed,including the stationary condition,constraint qualification and generalized convexity condition,and the relation between KKT point and S-stationary point of the mathematical program with switching constraint is discussed.Thirdly,the dual models of Wolfe type and Mond-Weir type are proposed for the mathematical program with switching constraint.Under the assumptions of convexity,strict convexity,quasi-convexity,pseudo-convexity and strict pseudoconvexity,the dual results of weak,strong,inverse,restricted inverse and strict inverse for two dual problems are described respectively.An example is given to demonstrate.Meanwhile,the sequential quadratic programming method is used to solve the mathematical program with switching constraint,and it is proved that the convergence point of the solution sequence of the subproblem is the Karush-Kuhn-Tucker point of the original problem under the linear independent constraint qualification of the subproblem.Finally,the numerical results show that the sequential quadratic programming method is feasible to deal with such problems.The last chapter summarizes the research results of this thesis and puts forward some problems that need to be further thought and solved in the future. |
