Topical and sub-topical functions, downward sets and abstract convexity

Optimization

Volumn 50, Issue 5-6, 2001, Pages 307-351

  Rubinov, A M ^a   Singer, I ^b  

^a UNIVERSITY OF BALLARAT   (Australia)

^b INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

Abstract convex functions; Abstract convex sets; Downward sets; Sub topical functions; Topical functions

Indexed keywords

EID: 0010810503     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

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2. Gondran, M. (1996). Analyse MINPLUS. Comptes Rendus Acad. Sci. (Paris), sér. 1, 323, 371-375.
3. Gunawardena, J. (1998). An introduction to idempotency. In: Idempotency (Gunawardena, J. (Ed.)), pp. 1-49, Cambridge University Press, Cambridge.
4. Gunawardena, J., From max-plus algebra to nonexpansive mappings: a non-linear theory for discrete event systems. Theoretical Computer Science, to appear (revised version of Technical Report HPL-BRIMS-99-07, Hewlett-Packard Labs., 1999).
5. Gunawardena, J. and Keane, M. (1995). On the existence of cycle times for some non-expansive maps. Technical Report HPL-BRIMS-95-003, Hewlett-Packard Labs.
6. Martínez-Legaz, J. -E., Rubinov, A. M. and Singer, I., Downward sets and their separation and approximation properties (submitted).
7. Martínez-Legaz, J. -E. and Singer, I. (1994). *-dualities. Optimization, 30, 295-315.
8. Martínez-Legaz, J. E. and Singer, I. (1997). On conjugations for functions with values in extensions of ordered groups. Positivity, 1, 193-218.
9. Pallaschke, D. and Rolewicz, S., Foundations of Mathematical Optimization. Convex Analysis without Linearity. Kluwer Academic Publishers, Dordrecht-Boston-London (1997).
10. Penot, J.-P. (1997). Duality for radiant and shady programs. Acta Math. Vietnamica, 22, 541-566.
11. Rubinov, A. M., Abstract Convexity and Global Optimization. Kluwer Academic Publishers, Boston-Dordrecht-London (2000).
12. Rubinov, A. M. and Singer, I. (2000). Best approximation by normal and conormal sets. J. Approx. Theory, 107, 212-243.
13. Singer, I., Abstract Convex Analysis, Wiley-Interscience, New York, 1997.