Seeking fast theoretical convergence and effective algorithms in unconstrained optimization is a very interested research topic for the optimization specialists and engineers. quasi-Newton method has been proved to be one of the most efficient methods when applied to unconstrained optimization by the favorable numerical experience and theoretics. Quasi-Newton equations play a key role in quasi-Newton methods for optimization problems. The original quasi-Newton equation employs only the gradient of the objective function, but ignores the available function value information.In this paper, a class of modified Quasi-Newton equations are derived, which apply both the gradient and function value. Moreover the Broyden quasi-Newton methods based on the class of modified quasi-Newton equations are proposed. Further observations are completed, such as heredity of positive-definite updates, global convergence, and superlinear convergence. In this paper, the global convergence analysis of restricted Broyden methods based on the class of modified Quasi-Newton equations is given. |