论文信息 - Further insight into the Shamanskii modification of Newton method

Further insight into the Shamanskii modification of Newton method

In this paper, a new Wolfe-type line search is proposed, and the global and superlinear of the Shamanskii method with the new line search are proved under mild assumptions. Furthermore, the iterative scheme of the Shamanskii method is also generalized.

[1] Carl Tim Kelley,et al. Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[2] Philip E. Gill,et al. Newton-type methods for unconstrained and linearly constrained optimization , 1974, Math. Program..

[3] Peter Deuflhard,et al. Numerische Mathematik. I , 2002 .

[4] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[5] V. Shamanskii. A modification of Newton's method , 1967 .

[6] Dimitri P. Bertsekas,et al. Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[7] Marco Sciandrone,et al. Global Convergence Technique for the Newton Method with Periodic Hessian Evaluation , 2001 .