TY - JOUR
T1 - Convergence criteria of the generalized newton method and uniqueness of solution for generalized equations
AU - Zhang, Yan
AU - Wang, Jinhua
AU - Guu, Sy Ming
N1 - Publisher Copyright:
© 2015.
PY - 2015
Y1 - 2015
N2 - Under a generalized L-average Lipschitz condition, we establish a convergence criterion around an initial point regarding the generalized Newton method for solving a generalized equation 0 ∈ F(x)+T(x), where F is Fréchet differentiable and T is set-valued and maximal monotone. Moreover, wc also get an estimation of uniqueness ball for a solution of the generalized equation. As applications, we obtain Kantorovich type theorem under the classical Lipschitz condition, convergence results under the γ-condition, and Smale's point estimate theory. Our results extend some corresponding results in [22].
AB - Under a generalized L-average Lipschitz condition, we establish a convergence criterion around an initial point regarding the generalized Newton method for solving a generalized equation 0 ∈ F(x)+T(x), where F is Fréchet differentiable and T is set-valued and maximal monotone. Moreover, wc also get an estimation of uniqueness ball for a solution of the generalized equation. As applications, we obtain Kantorovich type theorem under the classical Lipschitz condition, convergence results under the γ-condition, and Smale's point estimate theory. Our results extend some corresponding results in [22].
KW - Generalized Newton method
KW - Generalized equation
KW - Kantorovich type theorem
KW - The γ-condition
UR - https://www.scopus.com/pages/publications/84938094287
M3 - 文章
AN - SCOPUS:84938094287
SN - 1345-4773
VL - 16
SP - 1485
EP - 1499
JO - Journal of Nonlinear and Convex Analysis
JF - Journal of Nonlinear and Convex Analysis
IS - 7
ER -