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10,342
Computability of Convex Sets
 Proceedings of the 12th Symposium on Theoretical Aspects of Computer Science
, 1995
"... We investigate computability of convex sets restricted to rational inputs. Several quite different algorithmic characterizations are presented and proved to be equivalent, like the existence of effective approximations by polygons or effective line intersection tests. Also obtained are characterizat ..."
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Cited by 4 (0 self)
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We investigate computability of convex sets restricted to rational inputs. Several quite different algorithmic characterizations are presented and proved to be equivalent, like the existence of effective approximations by polygons or effective line intersection tests. Also obtained
Convex Sets and Convex Combinations
"... Summary. Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this a ..."
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Summary. Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction
Convex sets in acyclic digraphs
, 2008
"... A nonempty set X of vertices of an acyclic digraph is called connected if the underlying undirected graph induced by X is connected and it is called convex if no two vertices of X are connected by a directed path in which some vertices are not in X. The set of convex sets(connected convex sets) of ..."
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A nonempty set X of vertices of an acyclic digraph is called connected if the underlying undirected graph induced by X is connected and it is called convex if no two vertices of X are connected by a directed path in which some vertices are not in X. The set of convex sets(connected convex sets
Nonmonotone spectral projected gradient methods on convex sets
 SIAM Journal on Optimization
, 2000
"... Abstract. Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo–Lampariello–Lucidi nonmonotone lin ..."
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Cited by 215 (28 self)
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Abstract. Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo–Lampariello–Lucidi nonmonotone
On Visibility and Covering By Convex Sets
, 1999
"... A set X ` IR d is nconvex if among any n its points there exist two such that the segment connecting them is contained in X. Perles and Shelah have shown that any closed (n + 1)convex set in the plane is the union of at most n 6 convex sets. We improve their bound to 18n 3 , and show a lower ..."
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Cited by 6 (1 self)
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A set X ` IR d is nconvex if among any n its points there exist two such that the segment connecting them is contained in X. Perles and Shelah have shown that any closed (n + 1)convex set in the plane is the union of at most n 6 convex sets. We improve their bound to 18n 3 , and show a
Contraction and expansion of convex sets
 In proceedings of CCCG
, 2004
"... Helly’s theorem is one of the fundamental results in discrete geometry [9]. It states that if every � d + 1 sets in a set system S of convex sets in R d have nonempty intersection then all of the sets in S have ..."
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Cited by 3 (1 self)
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Helly’s theorem is one of the fundamental results in discrete geometry [9]. It states that if every � d + 1 sets in a set system S of convex sets in R d have nonempty intersection then all of the sets in S have
States of Convex Sets
, 2014
"... Abstract. State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–Moore algebras of the distribution monad. This article studies some computationally relevant properties of convex sets. We introduce the term effectus for a base category with suitable coproducts (so ..."
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Cited by 1 (1 self)
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Abstract. State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–Moore algebras of the distribution monad. This article studies some computationally relevant properties of convex sets. We introduce the term effectus for a base category with suitable coproducts (so
Clustered families of convex sets
 Houston J. Math
, 1989
"... Abstract. The ordinary and common notions of polarity of convex sets are remarkable among notions of polarity (not always having to do with convex sets) in that it is possible to give an easy condition on a family of (say) closed, convex sets containing the origin which insures that the union of the ..."
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Cited by 1 (0 self)
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Abstract. The ordinary and common notions of polarity of convex sets are remarkable among notions of polarity (not always having to do with convex sets) in that it is possible to give an easy condition on a family of (say) closed, convex sets containing the origin which insures that the union
Results 1  10
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10,342