A Modified Reduced Hessian SQP Method For Equality Constrained Optimization Based On Quasi-Newton Update Technique

In this thesis, we are concerned with equality constrained optimization prob-lems. It is well-known that the sequential quadratic programming(SQP) methodsare welcome for small and middle size problem. For large scale problem, how-ever, SQP method may not e?cient as even not over all. The reduced HessianSQP method can be applied to solve large scale problem due to its requirementof less space for storage. Existing reduced Hessian SQP methods are practicallye?cient. However, the conditions for a reduced Hessian SQP method are rigorous.In general the uniform positive definition of the reduced Hessian approximate isnecessary.In this thesis, basing on an MBFGS update for unconstrained optimization,we propose a way to construct quasi-Newton update for the reduced Hessian ap-proximating. In Chapter One, we introduce some well known iteration methodsincluding BFGS method. We then introduce the basis steps of the reduced HessianSQP method. In Chapter Two, we first introduce the MBFGS formula and thenapply it to the equality constrained problems. Under mild conditions, we prove theglobal convergence of the related reduced Hessian SQP method. We also obtainthe R-linear and two step super linear convergence of the proposed method. InChapter Three, by combining the MBFGS and CBFGS update formula, we pro-pose another update formula for the reduced Hessian approximation. The relatemethod retains the same convergence property as the method in Chapter Two.In Chapter Four, we also do some numerical experiments, the results show thee?ciency of the proposed methods.