An improved convex constrained conjugate gradient descent method for nonlinear monotone equations with signal recovery applications

The conjugate descent (CD) method is a conjugate gradient (CG) variant with remarkable convergence properties. This paper presents a modified CD scheme for solving systems of constrained monotone nonlinear equations. Eigenvalue analysis demonstrates that the proposed search direction matrix is positive definite. By incorporating the proposed algorithm with Solodov and Svaiter's projection method (1999), several convex-constrained monotone nonlinear equations were solved, yielding impressive results. The new algorithm exhibits descent properties and achieves global convergence under appropriate assumptions. Numerical comparisons with recent algorithms in the literature highlight the efficiency and effectiveness of the proposed method. Furthermore, the method is applied to signal recovery experiments in compressive sensing.