A Class Of Non-monotonic Amendments To The Quasi-newton Algorithm And Its Convergence Analysis

Quasi-Newton methods are regarded as the most efficient ones for solving unconstrained problems. In recent 20 years, many authors have made great efforts to study the Quasi-Newton methods. According to the linear search technique, the Quasi-Newton algorithm can be divided into monotone algorithm and non-monotone algorithm.Using the transformation of traditional Quasi-Newton equation and Taylor expansion, Xiaowei, fengjian Sun get a class of modified Quasi-Newton equation Using the BFGS formula and Wolf linear search technique, they get a class of modified Quasi-Newton algorithms. Under some suitable conditions, they prove the global and local super-linear convergence of the algorithms. Liu Han and Sun applied non-monotone linear search technique to the Quasi-Newton algorithm firstly. And under some suitable conditions, they prove the global and local super-linear convergence of the algorithms. Numerical experiment show that in some cases, non-monotone algorithm maybe more efficient than monotone one.In this paper, using the Non-monotone linear search technique and modified BFGS formula, we get a class of non-monotone modified Quasi-Newton algorithms based on the class of modified Quasi-Newton equation Xiaowei, fengjian Sun proposed. Under some suitable conditions, we prove the global and local super-linear convergence of our algorithms. At last, the numerical test results show that our algorithms are efficient for unconstrained optimization problems.