Another hybrid approach for solving monotone operator equations and application to signal processing
Poom Kumam, Auwal Bala Abubakar, Abdulkarim Hassan Ibrahim, Hamza Umar Kura, Bancha Panyanak, Nuttapol Pakkaranang
Abstract
This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.
Topics & Concepts
MathematicsLine searchConjugate gradient methodBenchmark (surveying)Convergence (economics)Bounded functionApplied mathematicsMonotone polygonOperator (biology)Descent directionNonlinear systemRegular polygonSIGNAL (programming language)AlgorithmNonlinear conjugate gradient methodMathematical optimizationSignal processingSignal reconstructionGradient descentMathematical analysisComputer scienceDigital signal processingArtificial intelligenceGeometryArtificial neural networkEconomic growthProgramming languageRepressorBiochemistryGeneGeodesyQuantum mechanicsComputer hardwarePhysicsComputer securityRADIUSTranscription factorEconomicsGeographyChemistrySparse and Compressive Sensing TechniquesNumerical methods in inverse problemsAdvanced Optimization Algorithms Research