Two Improved Conjugate Gradient Methods with Application in Compressive Sensing and Motion Control

Abstract

To solve the monotone equations with convex constraints, a novel multiparameterized conjugate gradient method (MPCGM) is designed and analyzed. This kind of conjugate gradient method is derivative-free and can be viewed as a modified version of the famous Fletcher–Reeves (FR) conjugate gradient method. Under approximate conditions, we show that the proposed method has global convergence property. Furthermore, we generalize the MPCGM to solve unconstrained optimization problem and offer another novel conjugate gradient method (NCGM), which satisfies the sufficient descent property without any line search. Global convergence of the NCGM is also proved. Finally, we report some numerical results to show the efficiency of two novel methods. Specifically, their practical applications in compressive sensing and motion control of robot manipulator are also investigated.

Projection method with inertial step for nonlinear equations: Application to signal recovery

“…In the following, we conduct a synthesized medium-scale LASSO experiment and we use the experiment parameters in [57]. Specifically, we set n = 2048, m = 512, and the original signal contains 64 randomly placed spikes.…”

Inertial-Based Derivative-Free Method for System of Monotone Nonlinear Equations and Application

“…Following the approach in [30], in the course of the motion control experiment, we take the length of the rod 1 = 2 = 1 and the end effector is controlled to track a Lissajous curve, which is expressed as…”

Motion control of the two joint planar robotic manipulators through accelerated Dai–Liao method for solving system of nonlinear equations

“…The proposed method clearly restored the disturbed signals in compressive sensing than the method proposed by Liu and Li (2015). Sun et al (2020), developed a method for solving the monotone equations with convex constraints. The proposed method can be viewed as a modified version of the famous Fletcher–Reeves (FR) conjugate gradient method.…”

“…Particularly, their practical applications in compressive sensing and motion control of robot manipulator. Following the approach in Sun et al (2020), Awwal et al (2020b) introduced inertial-based method for monotone nonlinear equations with application in motion control problem involving a two planar robot. Recently, Halilu et al (2021a) suggested some double direction methods for convex constrained monotone nonlinear equations with image restoration.…”