Best Approximation by Normal and Conormal Sets

Journal of Approximation Theory

Volumn 107, Issue 2, 2000, Pages 212-243

  Rubinov, A M ^a   Singer, I ^b  

^a UNIVERSITY OF BALLARAT   (Australia)

^b INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000078105     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.2000.3495     Document Type: Article

References (11)

1. Z. Dzalilov, A. M. Rubinov, and P. E. Kloeden, Lyapunov sequences and a turnpike theorem without convexity, Set-Valued Anal. 6 (1998), 277-302.
2. S. Karlin, "Mathematical Methods in Games, Programming and Economics," Pergamon, London/Paris, 1959.
3. A. M. Rubinov, "Superlinear Multivalued Mappings and Their Applications to Problems of Mathematical Economics," Nauka, Leningrad, 1980. [In Russian]
4. A. M. Rubinov and M. Yu. Andramonov, Minimizing increasing star-shaped functions based on abstract convexity, J. Global Optim., to appear.
5. A. M. Rubinov and B. M. Glover, Characterizing of optimality for homogeneous programming problems with applications, in "Recent Advances in Nonsmooth Optimization" (D.-Z. Du, L. Qi, and R. S. Womersley, Eds.), pp. 351-380, World Scientific, Singapore, 1995.
6. A. M. Rubinov and B. M. Glover, Duality for increasing positively homogeneous functions and normal sets, Rech. Opér/Oper. Res. 32 (1998), 105-123.
7. A. M. Rubinov, B. M. Glover, and V. Jeyakumar, A general approach to dual characterizations of solvability of inequality systems with applications, J. Convex. Anal. 2 (1995), 309-344.
8. I. Singer, "Abstract Convex Analysis," Wiley Interscience, New York, 1997.
9. I. Singer, "The Theory of Best Approximation and Functional Analysis," CBMS Reg. Confer. Ser. Appl. Math., Vol. 13, Soc. for Industr. App. Math., Philadelphia, 1974.
10. I. Singer, Duality in quasi-convex supremization and reverse convex infimization via abstract convex analysis, and applications to approximation, Optimization 45 (1999), 255-308.
11. M. Volle, Conjugaison par tranches et dualité de Toland, Optimization 18 (1987), 633-642.