Abstract
An extreme point property of optimal solutions of general concave programming problems is established that generalizes both Du-Hwang’s minimax theorem and its continuous version by Du and Pardalos.
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References
Bourbaki N. (1958). Espaces vectoriels topologiques, Hermann & Cie 1957, Paris. Interscience Piblishers, NewYork
Du D.Z. and Hwang F.K. (1990). The Steiner ratio conjecture of Gilbert-Pollak is true. Proceedings of National Academy of Sciences 87: 9464–9466
Du D.Z. and Pardalos P.M. (1994). A continuous version of a result of Du and Hwang. J. Global Optimization 5: 127–130
Du, D.Z., Pardalos, P.M., Wu, W.: Mathematical theory of optimization, Kluwer (2001)
Holmes R.B.: Geometric functional analysis and its application, Springer (1975)
von Neumann J. (1928). Zur Theorie der Gesellschaftsspiele. Math. Ann 100: 295–320
Tuy, H.: DC optimization: theory, methods and algorithms. In: Horst, R., Pardalos, P.M. (eds.) Handbook of global optimization, pp. 149–216. Kluwer (1995)
Tuy, H.: Convex analysis and global optimization, Springer (1998)
Tuy H. (2004). Minimax theorems revisited. Acta Mathematica Vietnamica 29: 217–229
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Tuy, H. Concave programming and DH-point. J Glob Optim 43, 407–413 (2009). https://doi.org/10.1007/s10898-007-9220-7
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DOI: https://doi.org/10.1007/s10898-007-9220-7
Keywords
- Steiner ratio
- Du-Hwang minimax theorem
- DH-point
- Du-Pardalos’ continuous version
- General concave programming
- DC programming
- Optimality condition