Two Kinds Of Modified Spectral Dy Conjugate Gradient Method

Optimization is widely and increasingly involved in economics, engineering, management, militaryand space technology and other areas. So, it is very valuable to construct computational methods, researchthe theoretical properties and study the computational performance of these numerical methods, especiallyfor large-scale optimization problem.In this thesis, we study two nonlinear self-scaling conjugate gradient methods for large-scaleoptimization problems. Since the self-scaling factor was chosen as the Hessian matrix’s Rayleigh quotientor its approximation, these self-scaling conjugate gradient methods were also called spectral conjugategradient methods.We review the current research of nonlinear conjugate gradient methods and spectral gradient methodsin Chapter1as well as some other usefull numerical computational methods. In Chapter2, we propose amodified spectral Dai-Yuan conjugate gradient (SVDY) method, which can generate a sufficient descentdirection under the Wolf line search, furthermore, we can establish the global convergence of this method.We choose some unconstrained optimization problems from CUTEr library to test the SVDY method. Thenumerical results in our paper show the method is effective and promising.In Chapter3, we present a new Hybrid spectral conjugate gradient (DS-HSDY) method. We can provethat this method is self-adjusting, and this property is independent of any line search. Although the searchdirection is not sufficient descent at every iteration, it is sufficient descent at most of the iterations. Undermild conditions, we prove that the method with Wolfe type line search converge globally fornonconvex functions. We also test this method for many unconstrained optimization problems fromCUTEr library. The numerical results show the method is effective and promising.