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Topic: Convex set

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convex hull

convex function

Locally convex topological vector space

Convex Computer

locally convex

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Proper convex function

Minimal convex decomposition

convex set

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Plano convex

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	PlanetMath: convex set
		Examples of convex sets in the plane are circles, triangles, and ellipses.
		A polyconvex set is a finite union of compact, convex sets.
		This is version 14 of convex set, born on 2001-10-15, modified 2007-06-18.
	planetmath.org /encyclopedia/ConvexSet.html (355 words)

	Convex Set Theoretic Image Recovery by Extrapolated Iterations of Parallel Subgradient Projections - COMBETTES ...
		Abstract: Solving a convex set theoretic image recovery problem amounts to finding a point in the intersection of closed and convex sets in a Hilbert space.
		The POCS algorithm, in which an initial estimate is sequentially projected onto the individual sets according to a periodic schedule, has been the most prevalent tool to solve such problems.
		R be a convex function, a real number, and g a selection of J, i.e.
	citeseer.ist.psu.edu /combettes97convex.html (896 words)

	Convex Sets (Site not responding. Last check: )
		A convex set is a set of elements from a vector space such that all the points on the straight line line between any two points of the set are also contained in the set.
		For whichever set c does not belong to this is a contradiction of that set's convexity, contrary to assumption.
		The significance of convex sets in economics is some theorems on the existence of separating planes and support planes for any convex set.
	www2.sjsu.edu /faculty/watkins/convex.htm (316 words)

	NationMaster - Encyclopedia: Convex set (Site not responding. Last check: )
		Convex Hull: Elastic band analogy // Alternative definitions In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X. (Note that X may be the union of any set of objects made of points).
		Closed convex sets can be characterised as the intersections of closed half-spaces (sets of point in space that lie on and to one side of a hyperplane).
		The definition of a convex set and a convex hull extends naturally to non-Euclidean geometry by defining a convex set to contain the geodesics joining any two points in the set.
	www.nationmaster.com /encyclopedia/Convex-set (1895 words)

	Convex Sets (Site not responding. Last check: )
		A convex set is a set of elements from a vector space such that all the points on the straight line line between any two points of the set are also contained in the set.
		For whichever set c does not belong to this is a contradiction of that set's convexity, contrary to assumption.
		The significance of convex sets in economics is some theorems on the existence of separating planes and support planes for any convex set.
	www.sjsu.edu /faculty/watkins/convex.htm (316 words)

	Quasi-Bayesian theory
		The convex combination of the elements of a set generates a convex set, which can be expressed as the convex hull of its vertices.
		The set of distributions maintained by an agent is called the credal set, and its existence is postulated on the grounds of axioms about preferences [Giron and Rios1980].
		Convex sets of conditional distributions are used to represent conditional beliefs.
	www.cs.cmu.edu /afs/cs/user/fgcozman/www/Research/QuasiBayesian/FiniteConvex/node4.html (487 words)

	2D Convex Hulls and Extreme Points (Site not responding. Last check: )
		In addition to the functions for producing convex hulls, there are a number of functions for computing sets and sequences of points related to the convex hull.
		Finally, a set of functions (ch_nswe_point, ch_ns_point, ch_we_point, ch_n_point, ch_s_point, ch_w_point, ch_e_point) is provided for computing extreme points of a 2D point set in the coordinate directions.
		Each of the functions used to compute convex hulls or extreme points is paramterized by a traits class, which specifies the types and geometric primitives to be used in the computation.
	www.ics.uci.edu /~dock/manuals/cgal_manual/Convex_hull_2/Chapter_main.html (803 words)

	Convex
		One application of convex hulls is found in efficiency frontier analysis[?].
		A convex function defined on some interval is continuous on the whole interval and differentiable at all but at most countably many points.
		One may compare this definition of convexity and that for sets, and note that a function is convex if, and only if, the region of the plane lying above the graph of said function is a convex set.
	www.ebroadcast.com.au /lookup/encyclopedia/co/Convex_hull.html (427 words)

	Convex Hull of a 2D Point Set or Polygon
		The convex hull of a geometric object (such as a point set or a polygon) is the smallest convex set containing that object.
		In this case, the boundary of a compact set is bounded by a polygon in 2D, and a polyhedron in 3D.
		The lower or upper convex chain is constructed using a stack algorithm almost identical to the one used for the Graham scan.
	geometryalgorithms.com /Archive/algorithm_0109/algorithm_0109.htm (2504 words)

	Convex Cones - Convex Optimization
		We call the set K a convex cone iff any nonnegative combination of elements from the cone remains in the cone.
		The set of all convex cones is a proper subset of all cones.
		The set of convex cones is a narrower but more familiar class of cone, any member of which can be equivalently described as the intersection of a possibly (but not necessarily) infinite number of hyperplanes (through the origin) and halfspaces whose bounding hyperplanes pass through the origin; a halfspace-description.
	www.convexoptimization.com /dattorro/convex_cones.html (167 words)

	On-Line Computer Graphics Notes
		convex combination of these points is also in the set.
		Since any convex combination of points from a convext set must lie in the set, then certainly the straight line joining any two points of the set must also be completely in the set.
		bounding box about the set of points, and since the bounding box is convex, we are insured that the convex-hull of the set of points is also contained in the bounding box.
	graphics.idav.ucdavis.edu /education/GraphicsNotes/Convex-Combinations/Convex-Combinations.html (441 words)

	3D Convex Hulls
		Both versions accept a range of input iterators defining the set of points whose convex hull is to be computed and a traits class defining the geometric types and predicates used in computing the hull.
		Then the number of points of the convex hull are obtained by counting the number of triangulation vertices incident to the infinite vertex.
		Notice that the vertices incident to the infinite vertex of the triangulation are on the convex hull but it may be that not all of them are vertices of the hull.
	www.cgal.org /Manual/3.2/doc_html/cgal_manual/Convex_hull_3/Chapter_main.html (727 words)

	Convex Structures
		However, convex structures are central in modern economics -- particularly with the development of linear programming and the discovery (by economists) of the Separating Hyperplane Theorem in the 1940s - which allowed them to reformulate much of the central tenets of Walrasian economics without unecessary and restrictive differentiability assumptions.
		Convexity was the organizing principle of mathematical economics - particularly as practiced by those associated with the Cowles Commission (Koopmans, Debreu, Arrow, etc.) throughout the 1950s.
		The dual convex cone is always closed regardless of whether the original convex cone is closed or not.
	cepa.newschool.edu /het/essays/math/convex.htm (1799 words)

	Convex Hull (Site not responding. Last check: )
		Planar convex hull programs can be made more efficient in practice using the observation than the leftmost, rightmost, topmost, and bottommost points must all be on the convex hull.
		The primary convex hull algorithm in the plane is the Graham scan.
		Reverse-search algorithms for constructing convex hulls are effective in higher dimensions [AF92], although constructions demonstrating the poor performance of convex hull algorithms for nonsimplicial polytopes are presented in [AB95].
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE185.HTM (1597 words)

	Convex set - AoPSWiki
		Informally, a convex set S is a set of points such that for any pair of points in the set, all the points between them (that is, on the line segment which joins them) are members of the set as well.
		The interior of circles and of all regular polygons are convex, but a circle itself is not because every segment joining two points on the circle contains points which are not on the circle.
		A region in a space which is not convex is called a concave set.
	www.artofproblemsolving.com /Wiki/index.php/Convex_set (223 words)

	Brian's Digest: Convexity
		The union of a finite set of closed sets is closed, but the union of an infinite set of closed sets might not be.
		By the way, Rockafellar defines the convex hull of a set S to be the intersection of all convex sets containing S. He defines this for the case S subset of R^n, but the definition may well pertain more generally, since the property that the intersection of convex sets is convex seems to be universal.
		The convex hull of X should be the minimal convex set containing X. Clearly it has to include finite convex combinations of points in X to be convex.
	www.worms.ms.unimelb.edu.au /digest/convexity.html (1068 words)

	All Elementary Mathematics - Study Guide - Sets - Basic notions. Examples of sets... (Site not responding. Last check: )
		A set and an element of a set concern with category of primary notions, for which it's impossible to formulate the strict definitions.
		For instance, a set of books in a library, a set of cars on a parking lot, a set of stars in the sky, a world of plants, a world of animals – these are examples of sets.
		An uncountable set is a set, elements of which can't be numbered.
	www.bymath.com /studyguide/sets/sec/sets1.htm (417 words)

	Computing Maximum-Area Sections of Convex Polyhedra - Definitions
		The smallest convex set containing all the points in S. The set of all convex combinations of the points in S. The intersection of all convex sets that contain all the points in S. These definitions all hold in R
		We can also define the convex hull of two or more polygons or polyhedra using the same definitions as above, simply by considering our set S to be the set of vertices of the union of our polygons or polyhedra.
		A polygon P is convex if it is simple (noncrossing) and if for all points x, y in P, the closed line segment xy is also in P. In more graphic terms, a polygon is convex if its boundary has no dents or depressions, when viewed from the outside.
	cgm.cs.mcgill.ca /~perouz/cs507/Projects/SamuliHeilala/definitions.html (1863 words)

	Perimeter of rounded convex planar sets (Site not responding. Last check: )
		A convex set is inscribed into a rectangle with sides a and 1/a so that the convex set has points on all four sides of the rectangle.
		The transformation also applied to the convex set, which now has the same area, and is inscribed into a square.
		We also look at the case when the inscribed convex set is a triangle.
	www.math-inst.hu /%7ecsirmaz/k.html (111 words)

	Your Website - Miscellaneous (Site not responding. Last check: )
		Convex Polygon In geometry, a convex polygon is a simple polygon whose interior is a convex set.
		Equivalently, a polygon is strictly convex if every line segment between two vertices of the polygon is strictly interior to the polygon except at its endpoints.
		Kite - a quadrilateral that has two distinct pairs of consecutive equilateral sides Midsegment of a Trapezoid - The midsegment of a trapezoid connects the midpoints of the two nonparallel sides of the trapezoid.
	maxpages.com /mathnotesmodb/Links - !http://maxpages.com/mathnotesmodb/Links (444 words)

	Convex (Site not responding. Last check: )
		Convex set, a set of points containing all line segments between each pair of points
		Convex function, a function with the epigraph (the set of points lying on or above the graph) forming a convex set
		Convex conjugate, is a generalization of the Legendre transformation
	www.dejavu.org /cgi-bin/get.cgi?ver=93&url=http://articles.gourt.com/%22http%3A%2F%2Farticles.gourt.com%2F%3Farticle%3Dconvex (183 words)

	CGAL Basic Library Reference Manual:
		The last parameter Traits in the convex hull and extreme point functions is a traits class that defines the primitives that are used in the algorithms.
		For the convex hull algorithm(s), postcondition check tests only convexity (if not disabled), but not containment of the input points in the polygon defined by the output points.
		Besides the default algorithm for computing convex hulls, implementations of some classical convex hull algorithms are available, with the same semantics as the default algorithm.
	www-graphics.stanford.edu /courses/cs368-00-spring/TA/manuals/CGAL/ref-manual2/ConvexHull/Chapter_main.html (1508 words)

	NationMaster - Encyclopedia: Dodecahedron (Site not responding. Last check: )
		In geometry, a Platonic solid is a convex regular polyhedron.
		It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section.
		An icosahedron noun (plural: -drons, -dra) is a polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral triangles as faces.
	www.nationmaster.com /encyclopedia/Dodecahedron (581 words)

	convex set - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "convex set" is defined.
		Convex Set : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include convex set: extreme subset of convex set
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=convex+set (91 words)

	Convex set - Math Help Forum
		Since there is no AB segment in set then set is concave.
		In the book there isn't definition of convex set, so I have read definition from one internet site which says that convex set is "a set of points in which all segments connecting points of the set lie entirely in the set".
		Since I had never heard of a concave set while I am very familiar with convex sets (which are frequently used in economics), my conclusion is that convexity is a well-established definition while concavity applied to a set is newer and less well-established.
	www.mathhelpforum.com /math-help/advanced-geometry/4863-convex-set.html (0 words)

	Convex Sets, Hyperplanes, and Various Hulls
		This activity is designed to help you understand how to recognize a convex set and draw a hyperplane and the linear, affine, conical, and convex hull of a set of points.
		The affine hull Aff(S) of a set S is the set of all affine combinations of vectors in S. It is the lowest dimensional hyperplane which passes through all the points of S. (I.e.
		The convex hull Conv(S) of a set S is the set of all convex combinations of vectors in S. Conv(S) is the smallest convex set containing the points of S. The convex hull of a finite set of points is called a Convex Polytope.
	www.saintmarys.edu /~psmith/338act7.html (777 words)

	lpch1def (Site not responding. Last check: )
		A convex set that can be enclosed in a rectangle.
		The intersection of a finite set of closed half-spaces is called a convex polyhedron.
		A point x in a convex set S is an extreme point if it is not an interior point of any line segment in S.
	math.nicholls.edu /badie/lpch1def.html (125 words)

	James-Stein type estimator by shrinkage to closed convex set with smooth boundary - Kuriki, Takemura (ResearchIndex)
		Abstract: We give James-Stein type estimators of multivariate normal mean vector by shrinkage to closed convex set K with smooth or piecewise smooth boundary.
		The rate of shrinkage is determined by the curvature of boundary of K at the projection point onto K.
		James-Stein type estimator by shrinkage to closed convex sets with smooth boundary.
	citeseer.ist.psu.edu /60292.html (665 words)

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