A new modified line search algorithm to solve large-scale non-smooth non-convex optimization problem

‎In this paper‎, ‎a new modified line search Armijo is used in the diagonal discrete gradient bundle method to solve large-scale non-smooth optimization 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 proposed 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.