AN IMPROVED INERTIAL PROJECTION METHOD FOR SOLVING CONVEX CONSTRAINED MONOTONE NONLINEAR EQUATIONS WITH APPLICATIONS

In this paper, combining the inertial technique and the projec-tion 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 direc-tion 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 ap-plication, applying it to solve the sparse signal problems in compressed sensing and the regularized decentralized logistic regression and the results are promis-ing.