Nonlinear Optimization Problems For A Class Of Projection Of Non-quasi-newton Algorithm

Finding high performance algorithms in nonlinear optimization is a very heated research topic for the optimization specialists. In recent years,papers [1,6,11,12,13,14] give a class of projection quasi-Newton algorithms by combining the projection methods and quasi-Newton method which have the superlinear convergence. Paper [2] gives a class of non-quasi-Newton algorithms about unconstrained programming problems based on the modified non-quasi-Newton equation. In this paper,we give a class of superlincarly convcngent algorithms for nonlinear programming problems with linear constrained by combining non-quasi-Newton methods with the projection methods.In chapter 1,we first introduce the development of optimization and some extensive optimality conditions which to decide the optimum solution. We review several extensive derivative descent methods of unconstrained programming and feasible descent methods of constrained programming.In chapter 2.we give a class of new algorithms for nonlinear programming problems with linear constrained by combining the gradient projection method with non-quasi-Newton method which was given in paper [2].It's global convergence and the superlinear convergence are proved under suitable conditions.In chapter 3,we give a class of new algorithms with inexact search for nonlinear programming problems with linear constrained by combining the generalized projection method with non-quasi-Newton method.It's global convergence and the superlinear convergence are proved under suitable conditions. The new algorthms avoid the transformation of axis and reduce the computions.