Smoothing Lipschitz functions

Optimization Methods and Software

Volumn 22, Issue 6, 2007, Pages 901-916

  Beliakov, Gleb ^a  

^a DEAKIN UNIVERSITY   (Australia)

Author keywords

Constrained approximation; Lipschitz approximation; Multivariate approximation; Scattered data approximation; Smoothing; Uniform approximation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; DATA REDUCTION; LINEAR PROGRAMMING; QUADRATIC PROGRAMMING;

CONSTRAINED APPROXIMATION; LIPSCHITZ APPROXIMATION; MULTIVARIATE APPROXIMATION; SCATTERED DATA APPROXIMATION; UNIFORM APPROXIMATION;

FUNCTION EVALUATION;

EID: 35148895118     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780701393591     Document Type: Article

References (21)

1. Alfeld, P., 1989, Scattered data interpolation in three or more variables. In: L.L. Schumaker and T. Lyche (Ed.) Mathematical Methods in Computer Aided Geometric Design (New York: Academic Press), pp. 1-34.
2. Cherkassky, V. and Mulier, F., 1998, Learning from Data (New York: Wiley).
3. Hastie, T., Tibshirani, R. and Friedman, J., 2001, The Elements of Statistical Learning (New York, Berlin, Heidelberg: Springer-Verlag).
4. Calvo, T., Kolesarova, A., Komornikova, M. and Mesiar, R., 2002, Aggregation operators: properties, classes and construction methods. In: T. Calvo, G. Mayor and R. Mesiar (Eds) Aggregation Operators. New Trends and Applications (Heidelberg, New York: Physica-Verlag), pp. 3-104.
5. Klement, E.P. and Kolesarova, A., 2005, Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators. Kybernetica, 41, 329-348.
6. Zimmermann, H.-J., 1996, Fuzzy Set Theory and its Applications (Boston: Kluwer).
7. Golomb, M. and Weinberger, H.F., 1959, Optimal approximation and error bounds. In: R.E. Langer (Ed.) On Numerical Approximation (Madison: The University of Wisconsin Press), pp. 117-190.
8. Micchelli, C.A. and Rivlin, T.J., 1977, A survey of optimal recovery. In: C.A. Micchelli and T.J. Rivlin (Eds) Optimal Estimation in Approximation (New York: Plenum Press), pp. 1-54.
9. Micchelli, C.A. and Rivlin, T.J., 1984, Lectures on optimal recovery. In: P.R. Turner (Ed) Numerical Analysis, volume 1129 of Lecture Notes in Mathematics (Heidelberg: Springer), pp. 12-93.
10. Traub, J.F. and Wozniakowski, H., 1980, A General Theory of Optimal Algorithms (New York: Academic Press).
11. Sukharev, A.G., 1992, Minimax Models in the Theory of Numerical Methods, volume 21 of Theory and Decision Library Series B (Dordrecht: Kluwer Academic Publishers).
12. Gaffney, P.W. and Powell, M.J.D., 1976, Optimal interpolation. In: G.A. Watson. (Ed.) Numerical Analysis, volume 506 of Lecture Notes in Mathematics (Heidelberg: Springer), pp. 90-99.
13. Weaver, N., 1999, Lipschitz Algebras (Singapore: World Scientific).
14. Gertz, E.M. and Wright, S.J., 2003, Object-oriented software for quadratic programming. ACM Transactions on Mathematical Software, 29, 58-81.
15. Beliakov, G., 2006, Interpolation of Lipschitz functions. Journal of Computational and Applied Mathematics, 196, 20-44.
16. Rubinov, A.M., 2000, Abstract Convexity and Global Optimization, volume 44 of Nonconvex Optimization and its Applications (Dordrecht; Boston: Kluwer Academic Publishers).
17. Demyanov, V.F. and Rubinov, A.M., 1995, Constructive Nonsmooth Analysis (Frankfurt am Main: Peter Lang).
18. Beliakov, G., 2005, Monotonicity preserving approximation of multivariate scattered data. BIT, 45, 653-677.
19. Gyorfi, L., Kohler, M., Krzyzak, A. and Walk, H., 2002, A Distribution-Free Theory of Nonparametric Regression (New York: Springer).
20. Bagirov, A., 1999, Derivative-free methods for unconstrained nonsmooth optimization and its numerical analysis. Journal Investigacao Operacional, 19, 75-93.
21. Bagirov, A., 2002, A method for minimization of quasidifferentiable functions. Optimization Methods and Software, 17, 31-60.