An inertial Dai-Liao conjugate method for convex constrained monotone equations that avoids the direction of maximum magnification

Abstract

This paper exploits the good features of the Dai-Liao (DL) conjugate gradient (CG) method in connection with the inertial interpolation and the projection technique to propose an efficient algorithm for solving the convex-constrained monotone system by avoiding the direction of maximum magnification (MM). It is well-known that if the gradient lies in the direction of MM by the search direction matrix, the algorithm may result in unnecessary computational errors and may likely not be convergent. Avoiding this direction will accelerate the convergence of the proposed algorithm theoretically and numerically. The proposed DL algorithm avoids the direction of MM and uses the inertial extrapolation and hyperplane projection steps to accelerate its convergence at every given iteration. The theoretical analysis proved that the proposed algorithm is globally convergent under some standard assumptions and has a linear convergence rate. Lastly, the numerical experiment on some test problems demonstrated that the algorithm is time-efficient and has less computational cost.