In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the m...

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we pres...

Frequency domain formulations of computational electromagnetic problems often require the solutions of complex-valued non-Hermitian systems of equations, which are still symmetric. For this kind of problems a whole class of sub-variant solver methods derived from the complex-valued Bi-Conjugate Gradient method is available. This class of methods contains established solution methods as the Conj...

Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. However, the strong Wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods. This paper presents a new version of the conjugate gradient method, which converges globally provided the line search satisses the standard Wolfe conditions. The condit...

Conjugate gradient methods are an important class of methods for solving unconstrained optimization problems, especially for large-scale problems. Recently, they have been studied in depth. In this paper, we further study the conjugate gradient method for unconstrained optimization. We focus our attention to the descent conjugate gradient method. This paper presents a modified conjugate gradien...

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based ...