Nonmonotone BFGS Method For Nonconvex Unconstrained Optimization

The purpose of the thesis is to study BFGS method in nonconvex with a nonmonotone line search for solving unconstrained optimization problems. We establish the convergence theorem of the proposed method. We also test the proposed method on a set of problems.In Chapter 2 , based on the modified quasi-Newton equation by Li and Fukushima, we propose a modified BFGS (MBFGS) method with a nonmonotone line search for nonconvex minimization. An attractive feature of the proposed method is that the condition for controling the acceptance of the next new iteration point will be more weaker, which the value of objective function needn't descend strictly at each iteration. We prove that the method globally convergents for slving nonconvex minimization problems without convex assumption on objective functions.The purposed of chapter 3 is to further study the method which proposed in chapter 2, under some appropriate conditions, we establish the superlinear convergence of the method. Numerical experiments show that the nonmonotone MBFGS method performs better than the monotone MBFGS method does.