Spectrum On Two Amendments To The Conjugate Gradient Algorithm

Optimization problem, which find the best strategy from the variety strategy, is widely used many disciplines and fields. Therefore, the construction of the optimization algorithm and the research of the algorithm's properation and numerical results have important value and meaning.The conjugate gradient method of the optimization problem is special studied in this paper.In Chapter 1, the optimization problem and the optimality conditions of the optimal solution are simply introduced; Several derivative decline algorithms of unconstrained optimization problem are reviewed. Finally,the conjugate gradient method is introduced .In chapter 2, the background and the current status of research of the spectrum conjugate gradient method are introduced,and the test functions used in this experiment are gived.In Chapter 3, two new spectrum conjugate gradient methods are proposed. In the first section, the two corrections of the spectrum conjugate gradient method is proposed based on the Neculai and Andrei.Doesn't depend on any line search, the new algorithm's sufficient descent can be proved. the global convergence of the algorithm is proved based on the Armijo line search. The numerical results of the new algorithm are superior to the spectrum DY algorithm and the FR method, the computation efficiency of the new algorithm can be comparable with the spectrum PRP algorithm. In the second section, two amendments of the PRP conjugate gradient method is proposed based in [58] (Cheng Wanyou). In the Armijo line search, the global convergence of the new algorithm is proved. The numerical results show that the new method has good computational efficiency.In Chapter 4, combing the two spectrums of the third chapter and the non-monotone line search, two new algorithms are given. the global convergences of the two new algorithms are proved. The numerical results of the two new algorithms are more effective in the non-monotone line search.