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Let be a convex subset of a real vector space and let : → be a function.. Then is called convex if and only if any of the following equivalent conditions hold: . For all ≤ ≤ and all , ∈, (+ (−)) ≤ + (−) ().The right hand side represents the straight line between (, ()) and (, ()) in the graph of as a function of ; increasing from to or decreasing from to sweeps this line.

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A convex mirror or diverging mirror is a curved mirror in which the reflective surface bulges towards the light source. Convex mirrors reflect light outwards, therefore they are not used to focus light. Such mirrors always form a virtual image, since the focal point (F) and the centre of curvature (2F) are both imaginary points "inside" the mirror, that cannot be reached.

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is convex (x[i] is ith largest component of x) Pointwise supremum If f (x,y) is convex in x for each y ∈ A, then g(x) = sup y∈A f(x,y) is convex In terms of epigraph: epi g = \ y∈A epi f (·,y) Examples support function of a set: S C(x) = supy∈ yTx f (x) = sup y∈C kx −yk λmax(X) = sup ku 2=1 u TXu where X ∈ Sn is convex. Minimization If f (x,y) is convex in (x,y) and C is a ...

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Convex Mirror. If the cut part of the hollow sphere is painted from inside, then its outer surface becomes the reflecting surface. This kind of mirror is known as a convex mirror. Characteristics of Convex Mirrors. A convex mirror is also known as a diverging mirror as this mirror diverges light when they strike on its reflecting surface.

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Convex Hulls in Large Databases In this section, we will introduce our two algorithms for the determination of the convex hull of a large point set which is stored in a multidimensional index. For our methods, we need hierarchical index structures such as the R-tree [18] or its variants. Our algorithms, however, do not exploit particular properties of R-trees such as the fact that the page ...

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convex (comparative more convex, superlative most convex) curved or bowed outward like the outside of a bowl or sphere or circle. 1837, William Whewell, History of the Inductive Sciences Drops of water naturally form themselves into figures with a convex surface. (mathematics, not comparable, of a set in Euclidean space) arranged such that for any two points in the set, a straight line between ...

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