Constrained Nonlinear Optimization Of Trust Region Filter SQP Algorithm

The constrained nonlinear programming (NLP) problem is an important research in numerical optimization fields. Many practical problems can be reduced to be the constrained nonlinear optimization problems. The filter SQP method which incorporated with trust region technic was initially proposed by Fletcher. The traditional SQP method whether LSQP or TSQP, all need to choose a suitablepenalty function as the cost function. Using the penalty function will usually penalty factor in choosing a penalty parameters need to be bounded, the boundary value, it is difficult to determine. In order to avoid the difficulties brought about by the penalty parameter, this kind of filter TSQP proposed by Fletcher do not need to use the penalty function as a value function, but consider filter can accept, so that we can avoid the difficulties caused by the penalty parameter selection. Fistly we introduce some basic theorices and conclusions of NLP problems inChaper1,including the iterative formulation,the optimization condition,the rate of convergence and the filter method. Next Chaper2proposes the construction of filter in the algorithm, the definition and properties of a Nonliner Complement Problem(NCP)function.Regarding to the NCP condition at a K-K-T point,we could construct a new constraint violation in each iterative point get a new filter. Thus a new filter SQP method is constructed.Such methods are characterrized by their use of the dominance concept of the multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.Restoration phase (firstly proposed by Fletcher) is needed by the method in this paper. A mechanism for proving global convergence in filter SQP method with the NCP function is described for constrained nonlinear optimization problem. We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions. In the third chapter gives the algorithm without penalty function and the structure of the filter method, namely the process of online search, adopt the method of penalty function and filter, constructing a new kind of penalty function and filter SQP algorithm. We proved that under the condition of the hypothesis, the new no penalty function and filter SQP algorithm has global convergence and Super linear convergence. The fifth chapter is this article conclusion and prospect.