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An assumption of convex position can make certain computational problems easier to solve. For instance, the traveling salesman problem , NP-hard for arbitrary sets of points in the plane, is trivial for points in convex position: the optimal tour is the convex hull. [ 3 ]
The concept of strong convexity extends and parametrizes the notion of strict convexity. Intuitively, a strongly-convex function is a function that grows as fast as a quadratic function. [11] A strongly convex function is also strictly convex, but not vice versa.
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.
Convexity (finance) - refers to non-linearities in a financial model. When the price of an underlying variable changes, the price of an output does not change linearly, but depends on the higher-order derivatives of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.
For sets of points in general position, the convex hull is a simplicial polytope. [ 21 ] According to the upper bound theorem , the number of faces of the convex hull of n {\displaystyle n} points in d {\displaystyle d} -dimensional Euclidean space is O ( n ⌊ d / 2 ⌋ ) {\displaystyle O(n^{\lfloor d/2\rfloor })} . [ 22 ]
Sleep experts discuss which positions are best and worst for back pain, sleep apnea, pregnancy, acid reflux, and more. What is the healthiest sleeping position? Sleep experts discuss which ...
In mathematics, the modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε-δ definition of uniform convexity as the modulus of continuity does to the ε-δ definition of continuity.