On the separation of convex sets in some idempotent semimodules

Linear Algebra and Its Applications

Volumn 435, Issue 7, 2011, Pages 1542-1548

  Briec, Walter ^a   Horvath, Charles ^a  

^a UNIVERSITÉ DE PERPIGNAN   (France)

Author keywords

B convexity; Geometric and functional separation; Hahn Banach like theorems; Halfspaces; Idempotent semimodules; Max Plus convexity

Indexed keywords

B-CONVEXITY; GEOMETRIC AND FUNCTIONAL SEPARATION; HAHN-BANACH LIKE THEOREMS; HALF SPACES; MAX-PLUS CONVEXITY; SEMIMODULES;

SET THEORY;

EID: 79958827005     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2010.01.018     Document Type: Article

References (6)

1. W. Briec, C.D. Horvath, and A. Rubinov Separation in B-convexity Pacific J. Optim. 1 2005 13 30
2. W. Briec, and C.D. Horvath Halfspaces and Hahn-Banach like properties in B-convexity and Max-Plus convexity Pacific J. Optim. 4 2 2008 293 317
3. C. Cohen, S. Gaubert, and J.P. Quadrat Hahn-Banach separation theorem for Max-Plus semimodules J.L. Menaldi, E. Rofman, A. Sulem, Optimal Control and Partial Differential Equations 2001 IOS Press
4. C. Cohen, S. Gaubert, and J.P. Quadrat Duality and separation theorems in idempotent semimodules Linear Algebra Appl. 379 2004 395 422
5. V. Nitica, and I. Singer The structure of Max-Plus hyperplanes Linear Algebra Appl. 426 2007 382 414 (Pubitemid 47259139)
6. S.N. Samborskii, G.B. Shpitz, Convex sets in the semimodule of bounded functions, in: V.P. Maslov, S.N. Samborskii (Eds.), Advances in Soviet Mathematics, vol. 13, 1992, pp. 135-137.