Inexact generalized Newton methods for second order C-differentiable optimization

Journal of Computational and Applied Mathematics

Volumn 93, Issue 2, 1998, Pages 107-122

  Pu, Dingguo ^a   Zhang, Jianzhong ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Convergence and convergence rate; Inexact generalized Newton method; Second order C dtfferentiable

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL OPERATORS; NONLINEAR PROGRAMMING; OPTIMIZATION; PROBLEM SOLVING;

INEXACT GENERALIZED NEWTON METHOD; OBJECTIVE FUNCTION;

DIFFERENTIATION (CALCULUS);

EID: 0032115745     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00064-8     Document Type: Article

References (11)

1. F.H. Clarke, Optimization and nonsmooth analysis, SIAM, Philadelphia, 1990.
2. R.S. Dembo, S.C. Eisenstat, T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal, 14 (1982) 400-408.
3. R.S. Dembo, T. Steihaug, Truncated-Newton algorithms for large-scale unconstrained optimization. Math. Programming 26 (1983) 190-212.
4. J.E. Dennis Jr., R.B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.
5. J.E. Dennis Jr., Jorge J. Moré, Quasi-Newton method, motivation and theory, SIAM Rev. 19 (1977) 46-89.
6. J.M. Martinez, L. Qi, Inexact Newton methods for solving nonsmooth equations, J. Comput. Appl. Math. 60 (1995) 127-145.
7. J.S. Pang, L. Qi, Nonsmooth equations: motivation and algorithms, SIAM J. Optim. 3 (1993) 443-465.
8. D. Pu, J. Zhang, Globally convergent inexact generalized Newton methods for non-twice differentiable optimization problems, Research Report MA-97-08, City University of Hong Kong, 1997. Presented at ISMP97, Lausanne, 1997.
9. L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations, Math. Oper. Res. 18 (1993) 227-244.
10. L. Qi, C-differential operators, C-differentiability and generalized Newton methods, AMR 96/5, Applied Mathematics Report, University of New South Wales, 1996.
11. L. Qi, J. Sun, A nonsmooth version of Newton's method, Math. Programming 58 (1993) 353-368.