A Class of Spectral Derivative‐Free Projection‐Based Methods with Inertial Strategy for Large‐Scale Constraint Nonlinear System of Monotone Equations and Applications to Image Restoration Problems

Combining the derivative‐free projection‐based method, the spectral strategy and the inertial technique, in this paper, a class of inertial spectral three‐term derivative‐free projection‐based methods are proposed for large‐scale constraint nonlinear system of monotone equations. The proposed methods are suitable for large‐scale problems without convexity and differentiability. Moreover, the sufficient descent property and the trust region property are satisfied independent of line search techniques. Meanwhile, the global convergence and the linearly convergent rate are established under standard conditions, respectively. 220 testing problems with feasible or infeasible initial points and the dimensions varying from 1000 to 100,000 are referred in the numerical experiment. Numerical results denote that the proposed methods are more effective and robust than the other derivative‐free projection‐based methods. Furthermore, the proposed methods are applied to some image restoration problems and the results also indicate that our methods are effective and promising.