%0 Journal Article %1 chen1998global %A Chen, Xiaojun %D 1998 %I SIAM %J SIAM journal on numerical analysis %K 49j25-optimal-control-problems-with-equations-with-ret-arguments 49m15-optimization-newton-type-methods 65h10-systems-of-nonlinear-algebraic-equations 65h20-global-methods-including-homotopy-approaches 65k05-numerical-mathematical-programming-methods 65k10-numerical-analysis-optimization-and-variational-techniques 65z05-applications-of-numerical-analysis-to-physics 90c25-convex-programming %N 3 %P 1130--1148 %T Global and superlinear convergence of inexact Uzawa methods for saddle point problems with nondifferentiable mappings %U https://epubs.siam.org/doi/abs/10.1137/S0036142995295789 %V 35 %X This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton--Uzawa method. We discuss applications of inexact Uzawa methods to separable convex programming problems and coupling of finite elements/boundary elements for nonlinear interface problems.

@article{chen1998global, abstract = {This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton--Uzawa method. We discuss applications of inexact Uzawa methods to separable convex programming problems and coupling of finite elements/boundary elements for nonlinear interface problems. }, added-at = {2024-03-26T04:18:58.000+0100}, author = {Chen, Xiaojun}, biburl = {https://www.bibsonomy.org/bibtex/2ba5d11f02189492287746a766011e20e/gdmcbain}, interhash = {ab0cf31e3fa90231307787549eb5ad9a}, intrahash = {ba5d11f02189492287746a766011e20e}, journal = {SIAM journal on numerical analysis}, keywords = {49j25-optimal-control-problems-with-equations-with-ret-arguments 49m15-optimization-newton-type-methods 65h10-systems-of-nonlinear-algebraic-equations 65h20-global-methods-including-homotopy-approaches 65k05-numerical-mathematical-programming-methods 65k10-numerical-analysis-optimization-and-variational-techniques 65z05-applications-of-numerical-analysis-to-physics 90c25-convex-programming}, number = 3, pages = {1130--1148}, publisher = {SIAM}, timestamp = {2024-03-26T04:21:57.000+0100}, title = {Global and superlinear convergence of inexact Uzawa methods for saddle point problems with nondifferentiable mappings}, url = {https://epubs.siam.org/doi/abs/10.1137/S0036142995295789}, volume = 35, year = 1998 }