Some Algothrom Theories And Application Of The Nonlinearly Constrained Optimization Problem

First, in this paper, by using Rosen projection matrix, the conditions are given on the scalars in memory gradient direction to ensure that the memory gradient projection direction is descent. A new memory gradient Rosen projection method for nonlinear programming with linear or nonlinear constraints is presented. The global convergence properties of the new method are discussed. Combining with conjugate gradient scalar and our new method, three new classes (FR, PR, HS) of memory gradient Rosen projection methods with conjugate gradient scalar are presented.Second, by using generalized projection rectify technique, correcting search direction by improved suppose conditions, a new one order correcting direction and combining with the SQP skill, a new SQP feasible descent algorithm for nonlinear in-equality constrained optimization problem (p) is presented, and under weaker conditions, we proved that the new methods are still global convergence and its strong convergence.The new methods use little storage, thus the methods are attractive for large-scale problems. The numerical results illustrate that the new methods are effective.