Convergence analysis of a proximal Gauss-Newton method

Abstract An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applications for solving constrained nonlinear equations are discussed and the numerical performance of the method is assessed on some significant test problems. Keywords Gauss-Newton method · Penalized nonlinear least squares · Proximity operator · Lipschitz conditions with L average Mathematics Subject Classification (2000) MSC 65J15 · MSC 90C30 · MSC 47J25

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Saverio Salzo, Silvia Villa
• Keywords: CORR 2011, Education, Mathematics Subject Classification, Nonlinear, Significant Test Problems