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Longer titles found: Logarithmically convex function (view), Quasiconvex function (view), Closed convex function (view), Proper convex function (view), Pseudoconvex function (view), K-convex function (view), Schur-convex function (view), Polyconvex function (view)

searching for Convex function 37 found (195 total)

alternate case: convex function

Hardy's theorem (155 words) [view diff] exact match in snippet view article find links to article

{\displaystyle 0<r<R,} then this function is strictly increasing and is a convex function of log ⁡ r {\displaystyle \log r} . Maximum principle Hadamard three-circle

Duality gap (844 words) [view diff] exact match in snippet view article find links to article

feasible set with its closed convex hull and with replacing a non-convex function with its convex closure, that is the function that has the epigraph

Stress majorization (1,171 words) [view diff] exact match in snippet view article find links to article

Leeuw's iterative majorization method at each step minimizes a simple convex function which both bounds σ {\displaystyle \sigma } from above and touches

Biconvex optimization (383 words) [view diff] exact match in snippet view article find links to article

generalization to functions of more than two arguments is called a block multi-convex function. A function f ( x 1 , … , x K ) → R {\displaystyle f(x_{1},\ldots

Newton's method in optimization (1,857 words) [view diff] exact match in snippet view article find links to article

the second derivative is positive, the quadratic approximation is a convex function of t {\displaystyle t} , and its minimum can be found by setting the

Information geometry (1,015 words) [view diff] exact match in snippet view article find links to article

Hessian metric (i.e a Riemannian metric given by the potential of a convex function). In this case, the manifold naturally inherits two flat affine connections

Uniformly smooth space (813 words) [view diff] exact match in snippet view article find links to article

_{X}(\varepsilon ):\varepsilon \in [0,2]\},\quad t\geq 0,} and the maximal convex function majorated by the modulus of convexity δX is given by δ ~ X ( ε ) =

Majda's model (503 words) [view diff] exact match in snippet view article find links to article

given flux function f = f ( w ) {\displaystyle f=f(w)} is a nonlinear convex function; the given ignition function ϕ = ϕ ( w ) {\displaystyle \phi =\phi

Omega ratio (862 words) [view diff] exact match in snippet view article find links to article

considers all moments. The standard form of the Omega ratio is a non-convex function, but it is possible to optimize a transformed version using linear

Gompertz distribution (1,388 words) [view diff] exact match in snippet view article find links to article

function h ( x ) = η b e b x {\displaystyle h(x)=\eta be^{bx}} is a convex function of F ( x ; η , b ) {\displaystyle F\left(x;\eta ,b\right)} . The model

Average absolute deviation (1,674 words) [view diff] exact match in snippet view article find links to article

[Y]\right)\leq \mathbb {E} \left[\varphi (Y)\right]} , where φ is a convex function, this implies for Y = | X − μ | {\displaystyle Y=\vert X-\mu \vert

Median (8,022 words) [view diff] exact match in snippet view article find links to article

for any random variable X with a finite expectation E[X] and for any convex function f f ( E ⁡ ( x ) ) ≤ E ⁡ ( f ( x ) ) {\displaystyle f(\operatorname

K-stability (8,333 words) [view diff] exact match in snippet view article find links to article

Any such toric test configuration can be elegantly described by a convex function on the moment polytope, and Donaldson originally defined K-stability

Hoeffding's lemma (693 words) [view diff] exact match in snippet view article find links to article

{\displaystyle a\leq 0\leq b} . Since e λ x {\displaystyle e^{\lambda x}} is a convex function of x {\displaystyle x} , we have that for all x ∈ [ a , b ] {\displaystyle

Coherent diffraction imaging (3,778 words) [view diff] exact match in snippet view article find links to article

Moreau-Yosida regularization, which is a method of turning a convex function into a smooth convex function (Moreau 1965) (Yosida 1964). The magnitude constraint

Poisson regression (2,750 words) [view diff] exact match in snippet view article find links to article

− ℓ ( θ ∣ X , Y ) {\displaystyle -\ell (\theta \mid X,Y)} , is a convex function, and so standard convex optimization techniques such as gradient descent

Uniform integrability (2,519 words) [view diff] exact match in snippet view article find links to article

uniformly integrable if and only if there exists a non-negative increasing convex function G ( t ) {\displaystyle G(t)} such that lim t → ∞ G ( t ) t = ∞ and

Katugampola fractional operators (2,748 words) [view diff] exact match in snippet view article find links to article

>0} and ρ > 0 {\displaystyle \rho >0} . If f {\displaystyle f} is a convex function on [ a , b ] {\displaystyle [a,b]} , then f ( a + b 2 ) ≤ ρ α Γ ( α

Carleman's inequality (1,078 words) [view diff] exact match in snippet view article find links to article

generalisation, due to Lennart Carleson, states the following: for any convex function g with g(0) = 0, and for any -1 < p < ∞, ∫ 0 ∞ x p e − g ( x ) / x

Geodesic (4,261 words) [view diff] exact match in snippet view article find links to article

variational problem. Indeed, E ( γ ) {\displaystyle E(\gamma )} is a "convex function" of γ {\displaystyle \gamma } , so that within each isotopy class of

Nikolay Krylov (mathematician, born 1941) (357 words) [view diff] exact match in snippet view article

in Sobolev Spaces, AMS 2008 The non-linearity can be modeled by a convex function. Krylov (1982). "Boundedly inhomogeneous elliptic and parabolic equations"

Logarithmic Sobolev inequalities (530 words) [view diff] exact match in snippet view article find links to article

{\textstyle F:\mathbf {C} ^{n}\rightarrow \mathbf {R} } be a smooth convex function. Then E F ( X ) e F ( X ) ≤ ( E e F ( X ) ) ( log ⁡ E e F ( X ) ) +

Quasi-arithmetic mean (1,936 words) [view diff] exact match in snippet view article find links to article

partitioning property of the mean. Consider a Legendre-type strictly convex function F {\displaystyle F} . Then the gradient map ∇ F {\displaystyle \nabla

Geodesic bicombing (688 words) [view diff] exact match in snippet view article find links to article

t\mapsto d(\sigma _{xy}(t),\sigma _{x^{\prime }y^{\prime }}(t))} is a convex function on [ 0 , 1 ] {\displaystyle [0,1]} for all x , x ′ , y , y ′ ∈ X {\displaystyle

Busemann function (12,928 words) [view diff] exact match in snippet view article find links to article

an explicit example which is not a proper metric space. If h is a convex function, Lipschitz with constant 1 and h assumes its minimum on any closed

Min-max theorem (4,542 words) [view diff] exact match in snippet view article find links to article

λ k ( A ) {\textstyle \lambda _{1}(A)+\dots +\lambda _{k}(A)} is a convex function, and ξ 1 ( A ) + ⋯ + ξ k ( A ) {\textstyle \xi _{1}(A)+\dots +\xi _{k}(A)}

Power cone (253 words) [view diff] exact match in snippet view article find links to article

programs. There are many problems that can be described as minimizing a convex function over a power cone. "MOSEK Modeling Cookbook - the Power Cones". Nesterov

Analytic function of a matrix (2,213 words) [view diff] exact match in snippet view article find links to article

definition is analogous to a concave scalar function. An operator convex function can be defined be switching ⪯ {\displaystyle \preceq } to ⪰ {\displaystyle

Factorial (8,432 words) [view diff] exact match in snippet view article find links to article

which states that the gamma function (offset by one) is the only log-convex function on the positive real numbers that interpolates the factorials and obeys

Classical general equilibrium model (756 words) [view diff] exact match in snippet view article find links to article

(hours worked) Let D(LS) be disutility from working, an increasing convex function with respect to LS. Consumption constraint = profit income + wage income

Gamma distribution (9,097 words) [view diff] exact match in snippet view article find links to article

Pedersen also proved many properties of the median, showing that it is a convex function of α, and that the asymptotic behavior near α = 0 {\displaystyle \alpha

Fisher information (7,377 words) [view diff] exact match in snippet view article find links to article

observations is n times the information in a sample of size 1. Given a convex function f : [ 0 , ∞ ) → ( − ∞ , ∞ ] {\displaystyle f:[0,\infty )\to (-\infty

Knapsack problem (7,799 words) [view diff] exact match in snippet view article find links to article

Kazuhisa; Guo, He (26 June 2014). "Online removable knapsack problem under convex function". Theoretical Computer Science. Combinatorial Optimization: Theory

Counterinsurgency (11,302 words) [view diff] exact match in snippet view article find links to article

argued, “will squash domestic opposition.” Treistman thus proposed a convex function to model the relationship between barbarism and counterinsurgency outcomes

Young's inequality for products (2,340 words) [view diff] exact match in snippet view article find links to article

follows immediately from the definition of the convex conjugate. For a convex function f {\displaystyle f} this also follows from the Legendre transformation

Jenkins–Traub algorithm (3,635 words) [view diff] exact match in snippet view article find links to article

R^{n}+|a_{n-1}|\,R^{n-1}+\dots +|a_{1}|\,R=|a_{0}|\,.} Since the left side is a convex function and increases monotonically from zero to infinity, this equation is

Barzilai-Borwein method (1,318 words) [view diff] exact match in snippet view article find links to article

solve some systems of linear and non-linear equations. To minimize a convex function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R}