FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations
Auwal Bala Abubakar, Kanikar Muangchoo, Abdulkarim Hassan Ibrahim, Jamilu Abubakar, Sadiya Ali Rano
Abstract
Abstract This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.
Topics & Concepts
MathematicsMonotone polygonLipschitz continuityOperator (biology)Euclidean spaceConjugate gradient methodNonlinear systemConvergence (economics)Descent directionType (biology)Monotonic functionRegular polygonConstraint (computer-aided design)Strongly monotoneApplied mathematicsMathematical optimizationGradient descentMathematical analysisComputer scienceGeneMachine learningPhysicsBiochemistryEconomic growthTranscription factorRepressorBiologyQuantum mechanicsEconomicsGeometryEcologyChemistryArtificial neural networkAdvanced Optimization Algorithms ResearchOptimization and Variational AnalysisIterative Methods for Nonlinear Equations