On strictly semi-monotone (semi-monotone) properties in nonsmooth functions

Applied Mathematics and Computation

Volumn 175, Issue 2, 2006, Pages 1609-1618

  Tawhid, M A ^a  

^a THOMPSON RIVERS UNIVERSITY   (Canada)

Author keywords

Generalized Jacobian; H Differentiability; Locally Lipschitzian; Nonlinear complementarity problems; Semi monotone; Semi smooth functions; Strictly semi monotone

Indexed keywords

NONLINEAR SYSTEMS; NUMERICAL METHODS; PROBLEM SOLVING;

GENERALIZED JACOBIAN; H-DIFFERENTIABILITY; LOCALLY LIPSCHITZIAN; SEMI-MONOTONE; SEMI-SMOOTH FUNCTIONS; STRICTLY SEMI-MONOTONE;

FUNCTIONS;

EID: 33645852234     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.09.008     Document Type: Article

References (17)

1. Clarke F.H. Optimization and Nonsmooth Analysis (1983), Wiley, New York (reprinted by SIAM, Philadelphia, PA, 1990)
2. Chen B., Chen X., and Kanzow C. A penalized Fischer-Burmeister NCP-function: Theoretical investigation and numerical results. Mathematical Programming 88 (2000) 211-216
3. Cottle R.W., Pang J.-S., and Stone R.E. The Linear Complementarity Problem (1992), Academic Press, Boston
4. M.S. Gowda, A Note on H-Differentiable Functions, Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, November, 1998.
5. Gowda M.S., and Ravindran G. Algebraic univalence theorems for nonsmooth functions. Journal of Mathematical Analysis and Applications 252 (2000) 917-935
6. Kanzow C., and Kleinmichel H. A new class of semismooth Newton-type methods for nonlinear complementarity problems. Computational Optimization and Applications 11 (1998) 227-251
7. Karamardian S. The complementarity problem. Mathematical Programming 2 (1972) 107-112
8. Mifflin R. Semismooth and semiconvex functions in constrained optimization. SIAM Journal on Control and Optimization 15 (1977) 952-972
9. Moré J.J., and Rheinboldt W.C. On P- and S-functions and related classes of N-dimensional nonlinear mappings. Linear Algebra and its Applications 6 (1973) 45-68
10. Qi L. Convergence analysis of some algorithms for solving nonsmooth equations. Mathematics of Operations Research 18 (1993) 227-244
11. L. Qi, C-Differentiability, C-Differential Operators and Generalized Newton Methods. Research Report, School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia, January 1996.
12. Qi L., and Sun J. A nonsmooth version of Newton's method. Mathematical Programming 58 (1993) 353-367
13. Rockafellar R.T. Convex Analysis (1970), Princeton University Press, Princeton
14. Rockafellar R.T., and Wets R.J.-B. Variational Analysis. Grundlehren der Mathematischen Wissenschaften 317 (1998), Springer-Verlag, Berlin
15. 0-properties in nonsmooth functions. Mathematics of Operations Research 25 (2000) 400-408
16. Tawhid M.A. On the local uniqueness of solutions of variational inequalities under H-differentiability. Journal of Optimization Theory and Applications 113 (2002) 149-164
17. Tawhid M.A., and Gowda M.S. On two applications of H-differentiability to optimization and complementarity problems. Computational Optimization and Applications 17 (2000) 279-299