64
Views
2
CrossRef citations to date
0
Altmetric
Miscellany

Mathematical diagnostics via nonsmooth analysis

Pages 197-218 | Received 29 Aug 2003, Accepted 07 Oct 2003, Published online: 31 Jan 2007

References

References

  • Vapnik V 2000 The Nature of Statistical Learning Theory New York Springer-Verlag
  • Bennett , KP and Mangasarian , OL . 1992 . Robust linear programming discrimination of two linearly inseparable sets . Optimization Methods and Software , 1 ( 1 ) : 22 – 34 .
  • Lee , Y-J and Mangasarian , OL . 2001 . SSVM: a smooth support vector machine for classification . Computational Optimization and Applications , 20 ( 1 ) : 5 – 22 .
  • Mangasarian , OL . 1994 . Misclassification minimization . Journal of Global Optimization , 5 : 309 – 323 .
  • Cucker , F and Smale , S . 2002 . On the mathematical foundations of learning . Bulletin (New Series) of the American Mathematical Society , 39 ( 1 ) : 1 – 49 .
  • Bagirov AM Rubinov AM Yearwood J 2002 A heuristic algorithm for feature selection based on optimization technique In: H. Abbass, C. Newton and R. Sarker (Eds) Heuristic and Optimization for Knowledge Discovery, Idea Group Publishing
  • Tsypkin Ya.Z 1973 Foundation of the Theory of Learning Systems (Trans.) Z.J. Nikolic New York Academic Press (original work published 1970)
  • Eremin , II . 1967 . A method of “penalties” in convex programming . Soviet Mathematics Doklady , 143 ( 4 ) : 748 – 751 .
  • Zangwill , WI . 1967 . Non-linear programming via penalty functions . Management Science , 13 : 344 – 358 .
  • Demyanov , VF , Di Pillo , G and Facchinei , F . 1998 . Exact penalization via Dini and Hadamard conditional derivatives . Optimization Methods and Software , 9 : 19 – 36 .
  • Demyanov VF Vasiliev LV 1985 Nondifferentiable Optimization New York Springer-Optimization Software
  • Demyanov VF Rubinov AM 1995 Constructive Nonsmooth Analysis Frankfurt a/M Verlag Peter Lang
  • Demyanov V Rubinov A (Eds), 2000 Quasidifferentiability and Related Topics Dordrecht/Boston/London Kluwer Academic Publishers
  • Schoelkopf B Burges CJC Smola AJ (Eds), 1999 Advances in Kernel Methods. Support Vector Learning Cambridge Mass. London The MIT Press
  • Cristianini N Shawe-Taylor J 2000 An Introduction to Support Vector Machines and Other Kernel Based Methods Cambridge Mass Cambridge University Press
  • Hiriart-Urruty J-B Lemarechal C 1993 Convex Analysis and Minimization Algorithms Berlin Springer
  • Pshenichnyi BN 1983 Method of Linearization (In Russian) Moscow Nauka
  • Rockafellar RT 1970 Convex Analysis Princeton NJ Princeton University Press
  • Kiwiel , KC . 1988 . Descent methods for quasidifferentiable minimization . Applied Mathematics and Optimization , 18 ( 2 ) : 163 – 180 .
  • Demyanov VF Astorino A Gaudioso M 2001 Nonsmooth problems in mathematical diagnostics In: N. Hadjisavvas, P.M. Pardalos (Eds), Advances in Convex Analysis and Global Optimization; Nonconvex Optimization and Its Applications 54 pp. 11–30 Dordrecht/Boston/London Kluwer Academic Publishers
  • Demyanov VF 2001 Identification of points of two convex sets Vestnik of St. Petersburg University, Ser. 1 Issue 3 (N 17), 14 20
  • Astorino , A and Gaudioso , M . 2002 . Polyhedral separability through successive LP . Journal of Optimization Theory and Applications , 112 ( 4 ) : 265 – 293 .
  • Rubinov AM Soukhoroukova NV Yearwood J 2001 Clustering for studying the structure and quality of datasets Research Report, University of Ballarat 24 January
  • Bagirov , A , Rubinov , A and Yearwood , J . 2001 . Using global optimization to improve classification for medical diagnosis . Topics in Health Information Management , 22 : 65 – 74 .
  • Kokorina , AV . 2003 . Ranking the parameters . TOP , 11 ( 1 ) : 86 – 89 .
  • Demyanov , AV , Demyanov , VF and Malozemov , VN . 2002 . Minmaxmin problems revisited . Optimization Methods and Software , 17 ( 5 ) : 783 – 804 .
  • Demyanov , VF . 1970 . On the solution of minimaximin problems . USSR Computational Mathamatics and Mathematical Physics , 10 ( 3 ) : 587 – 596 .
  • Demyanov , VF , Bagirov , AM and Rubinov , AM . 2002 . A method of truncated codifferential with application to some problems of cluster analysis . Journal of Global Optimization , 23 ( 1 ) : 63 – 80 .
  • Malozemov , VN and Pevnyj , AB . 1981 . On best piecewise-polynomial approximation . Vestnik Leningradskogo Universiteta Seriya Mathematika Mekhanika Astronomiya , 9 : 323 – 330 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.