The Algorithm Research On Nonlinear Optimization Problems

Since the past four decades, nonlinear optimization has been the mainstream in the international mathematical programming and one of branches of the most attention. It has a wide range of applications in defense, finance and management field, and many problems in other scientific fields can be attributed to nonlinear optimization problems,so the research to efficient algorithm for solving nonlinear optimization problems has important theoretical significance and social value.This thesis consists of five chapters,which are listed as follows:In chapter 1, the nonlinear programming are briefly introduced, and the algorithm of nonlinear programming problems mainly involved in the issues, complementarity problems and NCP functions are described;We give an overview of Lagrange - Newton method and Quasi-Newton method of the status quo In chapter 2; In chapter 3, an improved smooth NCP function replaced the weak complementary functions in the literature [15,16] and a new smooth Newton method is proposed, therefore the KKT conditions of the constraint optimization is transformed into an equivalent nonlinear equations.the Modified BFGS Algorithm proposed in literature [28] is used to make sure that its iterative matrix is positive definite, while avoiding the calculation of the workload of Hesse matrix,and It is proved that the algorithm is global convergence under certain conditions. In chapter 4,For the unconstrained optimization problems, a modified BFGS algorithm suitable for traditional quasi-Newton equation was generalized to the updated quasi-Newton equation after amending the iterative formula of Bk , which was Based on forced positive-definite idea. and thus a class of modified BFGS algorithm based on new quasi-Newton equation was presented. It was proved that this algorithm possessed global convergence under convex condition,and as a result, the requirements specified on the objective function was Reduced compared to the current article. In chapter 5, we summit our conclusion of this thesis.