A subspace inertial method for derivative-free nonlinear monotone equations

We introduce a subspace inertial line search algorithm (SILSA), for finding solutions of nonlinear monotone equations (NME). At each iteration, a new point is generated in a subspace generated by the previous points. Of all finite points forming the subspace, a point with the largest residual norm is replaced by the new point to update the subspace. In this way, SILSA leaves regions far from the solution of NME and approaches regions near it, leading to a fast convergence to the solution. This study analyzes global convergence and complexity upper bounds on the number of iterations and the number of function evaluations required for SILSA. Numerical results show that SILSA is promising compared to the basic line search algorithm with several known derivative-free directions.