Bilateral Correction Reduced Hessian Matrix Filter Affine Interior Point Method And Its Applications

Optimization theory and method, which makes research on how to find the optimal solution among many feasible plans, is very popular and useful subject. Optimization technology is wide-ly applied in many fields such as defense, industrial and agricultural production, transportation, financial, trade, management, scientific reach. With the development of the computers, opti-mization theory and method is playing an increasing role in practical application.In this paper, we use the filter idea introduced by Fletcher and Leyffer to solve non-negative nonlinear equality constrained problem and equality and inequality constrained nonlinear system-s.Fletcher and Leyffer proposed filter algorithm for solving nonlinear programming, instead of the traditional merit function method, as a tool to ensure the global convergence of algorithm for solving nonlinear programming. The main idea of this method is that trail points are accepted if they improve the objective function or improve the constraint violation instead of a combination of those two measures defined by a merit function.There are a few papers proposing interior-point methods for nonlinear programming. In this paper, we use an affine-scaling interior-point algorithm with a filter line-search method for solving non-negative nonlinear equality constrained programming and equality and inequality constrained nonlinear systems. The search direction of this algorithm is generated by first-order necessary conditions and a two-piece update of a projected reduced Hessian, a backtracking line search pro-cedure is used to generate step size. Local and global convergence is shown under some suitable conditions. Finally, we calculate some standard test examples by Matlab Software to illustrate the effectiveness of the proposed algorithm.The thesis consists of four parts. In Chapter 1, we summarize the basic concepts of optimiza-tion technique and the basic structure of the optimization method. In Chapter 2, we proposed two-piece update of a projected reduced Hessian algorithm with interior-point filter line-search technique for constrained optimization and proved the global and local convergence. In Chapter 3, we proposed two-piece update of a projected reduced Hessian algorithm with interior-point fil-ter line-search technique for equality and inequality constrained nonlinear systems and proved the global and local convergence. Finally, in Chapter 4, we conclude the main results of this thesis and propose some further research directions about our work.