A characterization of convexity-preserving maps from a subset of a vector space into another vector space

Journal of the London Mathematical Society

Volumn 64, Issue 1, 2001, Pages 179-190

  Ariyawansa, K A ^a   Davidon, W C ^c   McKennon, K D ^b  

^a WASHINGTON STATE UNIVERSITY   (United States)

^b Haverford College ^*  (United States)

^c HAVERFORD COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242698387     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0024610701002204     Document Type: Article

References (14)

1. K. A. ARIVAWANSA, W. C. DAVIDON and K. D. MCKENNON, 'On a characterization of convexity-preserving maps, Davidon's collinear scalings and Karraarkar's projective transformations ', Math. Programming, to appear (published online 17 January 2001, DOI 10.1007/S101070100212).
2. K. A. ARIYAWANSA, W. C. DAVIDON and K. D. MCKENNON, 'A coordinate-free foundation for projective spaces treating projective maps from a subset of a vector space into another vector space', Technical Report, Department of Pure and Applied Mathematics, Washington State University.
3. W. C. DAVIDON, 'Optimization by nonlinear scaling', Technical Report, Institutt for Teoretisk Fysikk, Trondheim, 1976.
4. W. C. DAVIDON, 'Optimization by nonlinear scaling', Proceedings of the Conference on Application of Numerical Software - Needs and Availability (ed. D. Jacobs, Academic Press, London, 1977) 377-383.
5. W. C. DAVIDON, 'Conic approximations and collinear scalings for optimizers', SIAM J. Numer. Anal. 17 (1980) 268-281.
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7. N. KARMARKAR, 'A new polynomial time algorithm for linear programming', Combinatorica 4 (1984) 373-395.
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9. K. NOMIZU, Fundamentals of linear algebra (McGraw-Hill, New York, 1966).
10. R. T. ROCKAFELLAR, Convex analysis (Princeton University Press, Princeton, NJ, 1970).
11. H. H. SCHAEFFER, Topological vector spaces (Macmillan, New York, 1966).
12. O. SCHREIER and E. SPERNER, Projective geometry of n dimensions (Chelsea, New York, 1961) (English translation by C. A. Rogers of the last chapter of Einfuhrung in die analytische Geometrie und Algebra (Königsberg, 1935)).
13. O. SCHREIER and E. SPERNER, Projective geometry of n dimensions (Chelsea, New York, 1961) (English translation by C. A. Rogers of the last chapter of Einfuhrung in die analytische Geometrie und Algebra (Königsberg, 1935)).
14. R. WEBSTER, Convexity (Oxford University Press, Oxford, 1994).