We introduce SILSA, a subspace inertial line search algorithm, 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.
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View A subspace inertial method for derivative-free nonlinear monotone equations