An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration
Abdulkarim Hassan Ibrahim, Poom Kumam, Auwal Bala Abubakar, Umar Yusuf Batsari, Seifu Endris Yimer, Kazeem Olalekan Aremu
Abstract
Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the global convergence of the sequence generated by the proposed algorithm. Applications and numerical example are presented to illustrate the performance of the proposed method.
Topics & Concepts
Monotonic functionConvergence (economics)Sequence (biology)Nonlinear systemProjection (relational algebra)Projection methodMathematicsRegular polygonAlgorithmDykstra's projection algorithmMathematical optimizationImage (mathematics)Computer scienceMathematical analysisArtificial intelligenceGeometryBiologyEconomic growthEconomicsPhysicsQuantum mechanicsGeneticsSparse and Compressive Sensing TechniquesAdvanced Image Processing TechniquesAdvanced Optimization Algorithms Research