The authors propose two limited memory BFGS algorithms with a nonmonotone line search technique for unconstrained optimization problems of the form \(\min_{x\in\mathbb{R}^n} f(x)\), where \(f: \mathbb{R}^n\to \mathbb{R}\) is continuously differentiable.
The global convergence of the given method is established under suitable conditions. Numerical results are given.