Geodesic
Minimization of Quadratic Functions on Convex Sets without Asymptotes
Journal of convex analysis, Tome 25 (2018) no. 2, pp. 623-641
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The classical Frank and Wolfe theorem states that a quadratic function which is bounded below on a convex polyhedron P attains its infimum on P. We investigate whether more general classes of convex sets F can be identified which have this Frank-and-Wolfe property. We show that the intrinsic characterizations of Frank-and-Wolfe sets hinge on asymptotic properties of these sets.
Classification : 90C20, 90C26
Mots-clés : Quadratic optimization problem, asymptotes, conic asymptotes, Motzkin decomposition, Frank and Wolfe theorem, complementarity problem 
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     author = {J.-E. Martinez-Legaz and D. Noll and W. Sosa},
     title = {Minimization of {Quadratic} {Functions} on {Convex} {Sets} without {Asymptotes}},
     journal = {Journal of convex analysis},
     pages = {623--641},
     year = {2018},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a14/}
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J.-E. Martinez-Legaz; D. Noll; W. Sosa. Minimization of Quadratic Functions on Convex Sets without Asymptotes. Journal of convex analysis, Tome 25 (2018) no. 2, pp. 623-641. http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a14/