Correction Of Spectral Ls Conjugate Gradient Algorithm And Its Application

In this thesis, we study the nonlinear spectral LS conjugate gradientmethod for large-scale unconstrained optimization problems and systems ofnonlinear equations. We investigated the global convergence of these methods,and applied a modified spectral LS conjugate gradient method to imagedenoising.First, we study a spectral LS conjugate gradient method for unconstrainedoptimization problems. Under some suitable conditions, we prove that themethod is globally convergent even if the nonlinear function is not strongconvex. This method can generate a sufficient descent direction and thisproperty is independent of line search used, Moreover, this method reduces tothe stand spectral LS conjugate gradient method if exact line search is used.In the next place, we extend the spectral LS conjugate gradient method tosolve large-scale nonlinear systems of equations. Then we proposed aderivative-free method,Under some mild conditions, we established the globalconvergence of this method.Finally, We consider the application of a modified spectral LS conjugategradient method in image denoising which based on two-phrase method., Thismethod use a step formula instead of the line search, Under some suitablecondition we prove the global convergence of this method. Our numericalexperiments show that this method is very effective and promising. Comparewith other methods, Our method can have the same denoising effect with lessCPU compute time.