Sequential Quadratic Programming Methods For Nonlinear Semi-infinite Programming

In this thesis, we mainly study to solve nonlinear semi-infinite programmingproblems by using sequential quadratic programming (SQP) methods. Semi-infinite programming includes either the number of decision variables or the num-ber of constraints is infinite, which is widely applied in many fields such as economicequilibrium, optimal control, information technology and computer network. Asthe development of high technology and the profound change of the social economy.More and more aspect are concerned with semi-infinite programming. Therefore,it is very important how to solve semi-infinite programming problems.It is well known that to solve nonlinear semi-infinite programming problemsis more complex than general nonlinear programming. There existed methodsinclude mainly discretization method, exchange method, local reduction method,SQP method etc. Among them, SQP method pays much attention. In the SQPmethod, the nonlinear semi-infinite programming problem is first transformed intononlinear programming problem by some discretization strategy and then to solvethe latter by employing the SQP method for nonlinear programming. However, theimplement of the method is very di?cult. Moreover, there exist many drawbacksin the existed SQP methods for nonlinear semi-infinite programming.In this thesis, we further study to solve nonlinear semi-infinite programmingproblems by using SQP method with Quasi-Newton technique and propose threeSQP type methods such as dual-SQP method based on the penalty function strat-egy, trust-region SQP method and Quasi-Newton SQP method. Moreover, weestablish the global convergence results for the proposed methods under mild con-ditions.The thesis consists of four chapters. In Chapter 1, we introduce some ba-sic theories and basic methods about semi-infinite programming problems. In thelater three chapters, we propose three SQP methods and analyze their global con-vergence under mild conditions, respectively.