Geodesic
A Mathematical Programming Approach to Strong Separation in Normed Spaces
Journal of convex analysis, Tome 17 (2010) no. 1, pp. 211-227 Cet article a éte moissonné depuis la source Heldermann Verlag

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This paper deals with an infinite-dimensional optimization approach to the strong separation of two bounded sets in a normed space. We present an approximation procedure, called Algorithm (A), such that a semi-infinite optimization problem must be solved at each step. Its global convergence is established under certain natural assumptions, and a stopping criterion is also provided. The particular case of strong separation in the space $L_{p} (\mathbb{X}, \mathcal{A}, \mu )$ is approached in detail. We also propose Algorithm (B), which is an implementable modification of Algorithm (A) for separating two bounded sets in $L_{p}([a,b])$, with $[a,b]$ being an interval in $\mathbb{R}$. Some illustative computational experience is reported, and a particular stopping criterion is provided for the case of functions of bounded variation in $L_{2}([a,b])$.
Classification : 90C48, 46A22, 90C90
Mots-clés : Strong separation, infinite dimensional optimization, semi-infinite programming 
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     author = {M. A. L\'opez and S.-Y. Wu and C. Ling and L. Qi},
     title = {A {Mathematical} {Programming} {Approach} to {Strong} {Separation} in {Normed} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {211--227},
     year = {2010},
     volume = {17},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_1_JCA_2010_17_1_a15/}
}
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M. A. López; S.-Y. Wu; C. Ling; L. Qi. A Mathematical Programming Approach to Strong Separation in Normed Spaces. Journal of convex analysis, Tome 17 (2010) no. 1, pp. 211-227. http://geodesic.mathdoc.fr/item/JCA_2010_17_1_JCA_2010_17_1_a15/