Descent PRP Conjugate Gradient Method For Large-scale Unconstrained Optimization And Constrained Monotone Equations

Conjugate gradient method is an important iterative method for solving optimizationproblems. It is particularly welcome in the solution of large-scale optimization problems. Agood property of the conjugate gradient method is its lower storage and good convergenceproperty. However, most existing conjugate gradient methods do not guarabtee to getdescent directions for the objective function. Although some have descent, But also verydependent on the algorithm used by line search. In this study, based on the conditions ofnew conjugate PRP conjugate gradient method, This method focuses on convergence andnumerical performance. there are four chapters in this paper.The first chapter, we brie?y introduced the background of the development of nu-merical optimization, Some notations used in this paper, Basic concepts, definitions andmain results.Chapter II, basing on Li, Tang and Wei amendment Ploak-Ribi`ere-Polyak (PRP)conjugate gradient method [1], we proposed to the new method of solving the problem ofnon-convex minimization. This method is characterized by a significant overall downwarddirection of the search, using Armijo-type line search prove this method having globalconvergence, And the algorithm has done a lot of numerical experiments. The resultsshow that our algorithm is very e?ective.Chapter III, we propose new PRP conjugate gradient algorithm for solving con-strained nonlinear monotone equations. The advantage of this is that it can be used tosolve large-scale nonlinear equations of the problem, And prove the global convergence ofthe algorithm.Chapter IV, though concluding this paper, we have further understanding of methodwith solving unconstrained nonlinear conjugate gradient and propose some worthwhile tocontinue research.