Arbitrary-norm separating plane

Operations Research Letters

Volumn 24, Issue 1, 1999, Pages 15-23

  Mangasarian, O L ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FUNCTIONS; LINEAR PROGRAMMING; POLYNOMIALS; PROBLEM SOLVING; SET THEORY;

ARBITRARY-NORM DISTANCES; FINITE SUCCESSIVE LINEARIZATION ALGORITHMS; SEPARATING PLANES;

OPERATIONS RESEARCH;

EID: 0032686461     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(98)00049-2     Document Type: Article

References (25)

1. E.F. Beckenbach, R. Bellman, Inequalities, Springer, Berlin, 1961.
2. Bennett K.P., Mangasarian O.L. Robust linear programming discrimination of two linearly inseparable sets. Optim. Meth. Software. 1:1992;23-34.
3. Bennett K.P., Mangasarian O.L. Bilinear separation of two sets in n-space. Comput. Optim. Appl. 2:1993;207-227.
4. P.S. Bradley, O.L. Mangasarian, W.N. Street, Clustering via concave minimization, in: M.C. Mozer, M.I. Jordan, T. Petsche (Eds.), Advances in Neural Information Processing Systems -9-, MIT Press, Cambridge, MA, 1997, pp. 368-374. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/96-03.ps.Z.
5. Bramley R., Winnicka B. Solving linear inequalities in a least square sense. SIAM J. Sci. Comput. 17:1996;275-286.
6. A. Charnes, Some fundamental theorems of perceptron theory and their geometry, in: J.T. Lou, R.H. Wilcox (Eds.), Computer and Information Sciences, Spartan Books, Washington, D.C., 1964, pp. 67-74.
7. Frank M., Wolfe P. An algorithm for quadratic programming. Naval Res. Logistics Q. 3:1956;95-110.
8. Glover F. Improved linear programming models for discriminant analysis. Decision Sci. 21:1990;771-785.
9. Grinold R.C. Mathematical methods for pattern classification. Management Sci. 19:1972;272-289.
10. J. Hertz, A. Krogh, R.G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, Redwood City, CA, 1991.
11. Karmarkar N. A new polynomial time algorithm for linear programming. Combinatorica. 4:1984;373-395.
12. Mangasarian O.L. Linear and nonlinear separation of patterns by linear programming. Oper. Res. 13:1965;444-452.
13. O.L. Mangasarian, Multi-surface method of pattern separation, IEEE Trans. Inform. Theory IT-14 (1968) 801-807.
14. O.L. Mangasarian, Nonlinear Programming, McGraw-Hill, New York, 1969. Reprint: SIAM Classic in Applied Mathematics 10, 1994, Philadelphia.
15. O.L. Mangasarian, Some applications of penalty functions in mathematical programming, in: R. Conti, E. De Giorgi, F. Giannessi (Eds.), Optimization and Related Fields, Lecture Notes in Mathematics, vol. 1190, Springer, Heidelberg, 1986, pp. 307-329.
16. Mangasarian O.L. Misclassification minimization. J. Global Optim. 5:1994;309-323.
17. Mangasarian O.L. The linear complementarity problem as a separable bilinear program. J. Global Optim. 6:1995;153-161.
18. O.L. Mangasarian, Arbitrary-norm separating plane, Technical Report 97-07, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, May 1997. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/97-07.ps.Z.
19. O.L. Mangasarian, J.-S. Pang, Exact penalty functions for mathematical programs with linear complementarity constraints, Optimization 42 (1997) 1-8. //ftp.cs.wisc.edu/math-prog/tech-reports/96-06.ps.Z.
20. O.L. Mangasarian, R. Setiono, W.H. Wolberg, Pattern recognition via linear programming: theory and application to medical diagnosis, in: T.F. Coleman, Y. Li, (Eds.), Large-Scale Numerical Optimization, SIAM, Philadelphia, PA, 1990, pp. 22-31. Proceedings of the Workshop on Large-Scale Numerical Optimization, Cornell University, Ithaca, New York, 19-20 October 1989.
21. Motzkin T.S., Schoenberg I.J. The relaxation method for linear inequalities. Can. J. Math. 6:1954;393-404.
22. N.J. Nilsson, Learning Machines, MIT Press, Cambridge, MA, 1966.
23. R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
24. G.W. Stewart, Introduction to Matrix Computations, Academic Press, New York, 1973.
25. R.J. Vanderbei, Linear Programming: Foundations and Extensions, Kluwer Academic Publishers, Hingham, MA, 1997.