A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration

Abstract

This paper proposes a novel hybrid PRP-HS-LS-type conjugate gradient algorithm for solving constrained nonlinear systems of equations. The proposed algorithm presents several significant advancements and key features: (i) the conjugate parameter is constructed by utilizing the hybrid technique; (ii) the search direction, designed with the conjugate parameter, possesses sufficient descent and trust region properties without the need for a line search mechanism; (iii) the global convergence is rigorously established under general assumptions, notably without the requirement of the Lipschitz continuity condition; (vi) numerical experiments demonstrate the algorithm's efficiency, particularly in solving large-scale constrained nonlinear systems of equations and addressing the sparse signal restoration problem.

Keywords

• constrained nonlinear systems of equations
• conjugate gradient method
• large-scale
• global convergence
• signal reconstruction