Solving Unconstrained Optimization Problems Spectral Conjugate Gradient Algorithm

The spectrum conjugate gradient method is widely used in many disciplinesand fields. Spectrum conjugate gradient method is a method that combinesspectrum gradient method and conjugate gradient method, It can produce adescent direction; A quadratic function is R-super linear convergence; Andnumerical experiments show that it has good computing efficiency. So themethod is simple and effective. In view of these advantages of the spectrumconjugate gradient method, therefore spectrum conjugate gradient method iswidely used in large scale optimization areas.This paper makes a study of the thought and improvement of the spectrumconjugate gradient method, The spectrum coefficient is introduced to WYLconjugate gradient method and the hybrid conjugate gradient method of thepaper [39], then two spectrum conjugate gradient methods are proposed. and wediscuss their global convergence and effectiveness in different line search.In Chapter1, the optimization problem and the optimality conditions ofthe optimal solution are simply introduced; several derivative declinealgorithms of unconstrained optimization problem are reviewed. Finally, theconjugate gradient method is introduced.In chapter2, the background and the current status of research of thespectrum conjugate gradient method are introduced, and the test functions usedin this experiment are given.In Chapter3, Based on WYL conjugate gradient formula, a newspectral kis proposed in this paper. In the Armijo line search, the globalconvergence of the new algorithm is proved. The numerical results show that thenew method has good computational efficiency.In Chapter4, Based on chapter III of this chapter, the global convergence ofthe new algorithm SWYL is proved in the Wolfe line search.In Chapter5,The mixing the conjugate gradient method is proposed based on a spectrum of hybrid conjugate gradient method, we prove its globalconvergence, the numerical experiments show that the two methods presented inthis chapter are valid.