Three adaptive hybrid derivative‐free projection methods for constrained monotone nonlinear equations and their applications
Pengjie Liu, Xiaoyu Wu, Hu Shao, Yan Zhang, Shuhan Cao
Abstract
Abstract In this work, by considering the hyperplane projection and hybrid techniques, three scaled three‐term conjugate gradient methods are extended to solve the system of constrained monotone nonlinear equations, and the developed methods have the advantages of low storage and only using function values. The new methods satisfy the sufficient descent condition independent of any line search criterion. It has been proved that three new methods converge globally under some mild conditions. The numerical experiments for constrained monotone nonlinear equations and image de‐blurring problems illustrate that the proposed methods are numerically effective and efficient.
Topics & Concepts
MathematicsLine searchMonotone polygonHyperplaneNonlinear systemConjugate gradient methodProjection methodDescent directionProjection (relational algebra)Applied mathematicsMathematical optimizationDescent (aeronautics)Gradient descentAlgorithmDykstra's projection algorithmComputer scienceGeometryArtificial neural networkEngineeringComputer securityAerospace engineeringMachine learningRADIUSPhysicsQuantum mechanicsAdvanced Optimization Algorithms ResearchSparse and Compressive Sensing TechniquesIterative Methods for Nonlinear Equations