Sharif Digital Repository

We describe two modified secant equations proposed by Yuan, Li and Fukushima. First, we study the approach proposed by Andrei. Then, we explain two hybrid conjugate gradient methods for unconstrained optimization problems. The methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. It is shown that one of the algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. Two approaches for computing the initial value of the steplength proposed by Babaie, Fatemi, and Mahdavi-Amiri and Andrei are used for accelerating the performance of the line search. We implement the algorithms and compare the... 

Nonlinear optimization is concerned with finding optimal solutions of optimization problems, where the objective function or some constraints are nonlinear. Since many issues in science and engineering can be expressed and formulated as a nonlinear problem, we investigate BFGS method, a successful iterative quasi-Newton method, for solving non-convex problems in unconstrained optimization. The method is based on the work of Yuan and his colleagues, making use of modified weak Wolfe-Powell line search, introducing a certain condition, introducing the next point if the condition is met, introducing a parabolic function if the condition is not established and obtaining the projection point and...