algorithm for finding an ε {\displaystyle \varepsilon } approximation to the volume of a convex body K {\displaystyle K} in n {\displaystyle n} -dimensional...

volume can be computed approximately, for instance, using the convex volume approximation technique, when having access to a membership oracle. As for...

problem is called structured low rank approximation. The more general form is named convex-restricted low rank approximation. This problem is helpful in solving...

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

reduced to polygonal approximations. In either case, it is computationally wasteful to test each polygon against the view volume if the object is not...

geometry asymptotic theory of convex bodies approximation by convex sets variants of convex sets (star-shaped, (m, n)-convex, etc.) Helly-type theorems and...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

1991 from Carnegie Mellon University, with a dissertation on convex volume approximation supervised by Ravindran Kannan. Applegate worked on the faculty...

adaptive algorithm for Klee's measure problem. Convex volume approximation, an efficient algorithm for convex bodies Klee, Victor (1977), "Can the measure...

mathematics, a convex body in n {\displaystyle n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a compact convex set with non-empty...

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are...

statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to the origin and which has volume greater than 2 n...

analogous approximation of convex sets by tangent cones to sets" that can be non‑smooth or non‑convex. Economists have also used algebraic topology. Convex duality...

answer is given only approximately. To define the approximation, we define the following operations on convex sets:: 6  S(K,ε) is the ball of radius ε around...

bounding volume. "Smallest" may refer to volume, area, perimeter, etc. of the box. It is sufficient to find the smallest enclosing box for the convex hull...

the historical cases. Convex duality Duality Relaxation (approximation) Boyd, Stephen P.; Vandenberghe, Lieven (2004). Convex Optimization (pdf). Cambridge...

complex numbers Gamma function: Lanczos approximation Spouge's approximation — modification of Stirling's approximation; easier to apply than Lanczos AGM method...

Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning...

positive reals, which is logarithmically convex, meaning that y = log ⁡ f ( x ) {\displaystyle y=\log f(x)} is convex. The notation Γ ( z ) {\displaystyle...

Frieze and Ravindran Kannan for random-walk-based approximation algorithms for the volume of convex bodies. Alfred Lehman for 0,1-matrix analogues of...

more is true as shown below (Lipschitz approximation). The above property for uniformly continuous function on convex domains admits a sort of converse at...

method for minimizing convex functions over convex sets. The ellipsoid method generates a sequence of ellipsoids whose volume uniformly decreases at...

algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine...

The center-of-gravity method is a theoretic algorithm for convex optimization. It can be seen as a generalization of the bisection method from one-dimensional...

any continuous function f {\displaystyle f} mapping a nonempty compact convex set to itself, there is a point x 0 {\displaystyle x_{0}} such that f (...

Minkowski sum is approximately convex. Related results provide more refined statements about how close the approximation is. For example, the Shapley–Folkman...

convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on producers with convex production sets; for convex...

an ε-approximation of the Pareto-front P, if the directed Hausdorff distance between S and P is at most ε. They observe that an ε-approximation of any...

is also an excellent approximation to π, attributed to Chinese mathematician Zu Chongzhi, who named it Milü. This approximation is better than any other...

although they have equal volume. Like the cells in Kelvin's structure, these cells are combinatorially equivalent to convex polyhedra. One is a pyritohedron...