Jean B. Lasserre
Abstract
(Positively) homogeneous functions play a special role in the Legendre-Fenchel duality. The Legendre-Fenchel conjugate of a p-homogeneous function is a q-homogeneous function with 1/p+1/q= 1. Further properties of the function, its conjugate, and of the maximizers are also derived. The same result also holds in the Max-Prod and Min-Max algebra for the analogue of the Legendre-Fenchel transform.
Author information
Jean B. Lasserre
References
- J. P. Aubin: L'Analyse Non-linéaire et ses Motivations Economiques, Masson, Paris, 1984.Google Scholar
- F. Bacelli, G. Cohen, G. J. Olsder, J. P. Quadrat: Synchronization and Linearity, Wiley, 1992.Google Scholar
- R. Bellman, W. Karush: On a new functional transform in analysis: the maximum transform, Bull. Amer. Math. Soc. 67 (1961) 501-503.https://doi.org/10.1090/S0002-9904-1961-10657-5Google Scholar
- R. Bellman, W. Karush: Mathematical programming and the maximum transform, SIAM J. Appl. Math. 10 (1962) 550-567.https://doi.org/10.1137/0110042Google Scholar
- T. Huillet, G. Salut: Optimal versus random processes, LAAS-Report 89189, June 1989.Google Scholar
- P. Del Moral, G. Salut: Maslov optimization theory, LAAS-Report 94461, Nov. 1994. To appear in Russian J. of Math. Phys.Google Scholar
- M. Gondran: Analyse MINPLUS, C. R. Acad. Sci. Paris, Série 1, 233 (1996) 371-375.Google Scholar
- M. Gondran: Analyse MINMAX, C. R. Acad. Sci. Paris, Série 1, to appear.Google Scholar
- J. B. Hiriart-Urruty, C. Lemaréchal: Convex Analysis and Minimization Algorithms, Springer-Verlag, Berlin, 1993.https://doi.org/10.1007/978-3-662-02796-7Google Scholar
- P. J. Laurent: Approximation et Optimisation, Hermann, Paris, 1972.Google Scholar
- V. Maslov, S. N. Samborski: Idempotent analysis, Adv. in Soviet Math. 13, Amer. Math. Soc., 1992.https://doi.org/10.1090/advsov/013Google Scholar
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Published by Heldermann Verlag, 1998. Rights now held by Banach Press LLC.
