An improved inertial projection method for solving convex constrained monotone nonlinear equations with applications.

In this paper, combining the inertial technique and the projection strategy, we propose an improved inertial projection method for solving convex constrained monotone nonlinear equations. The direction obtained by embedding the inertial extrapolation step into the design of the search direction satisfies the independent sufficient descent property under any line search. The global convergence of the proposed method is theoretically investigated. Numerical comparisons with the other four methods show that the proposed algorithm has superior numerical performance. In addition, as a practical application, applying it to solve the sparse signal problems in compressed sensing and the regularized decentralized logistic regression and the results are promising. [ABSTRACT FROM AUTHOR]