A New Non-monotone Line Search Algorithm to Solve Non-smooth Optimization Finance Problem

In this paper, a new non-monotone line search is used in the diagonal discrete gradient bundle method to solve large-scale non-smooth optimization problems. Non-smooth optimization problems are encountered in many applications in fi-nance problems. The new principle causes the step in each iteration to be longer, which reduces the number of iterations, evaluations, and the computational time. In other words, the efficiency and performance of the method are improved. We prove that the diagonal discrete gradient bundle method converges with the pro-posed non-monotone line search principle for semi-smooth functions, which are not necessarily differentiable or convex. In addition, the numerical results confirm the efficiency of the proposed correction.