subderivatives (or subgradient) generalizes the derivative to convex functions which are not necessarily differentiable. The set of subderivatives at...

many subderivatives at zero, with just one of them taking the value sgn ⁡ ( 0 ) = 0 {\displaystyle \operatorname {sgn}(0)=0} . A subderivative value...

Convex function Invex function Legendre transformation Semi-continuity Subderivative Main results (list) Carathéodory's theorem Ekeland's variational principle...

at each real number x {\displaystyle x} we have a nonempty set of subderivatives, which may be thought of as lines touching the graph of φ {\displaystyle...

Let S {\displaystyle S} be a nonempty set of primes. The arithmetic subderivative of x {\displaystyle x} with respect to S {\displaystyle S} is defined...

for problems of differential equations and in functional analysis. Subderivative Weyl's lemma (Laplace equation) Evans, Lawrence C. (1998). Partial differential...

{\displaystyle h_{j}\colon \mathbb {R} ^{n}\rightarrow \mathbb {R} } have subderivatives at a point x ∗ ∈ R n {\displaystyle x^{*}\in \mathbb {R} ^{n}} . If...

required, in which conventional derivatives are replaced by (set-valued) subderivatives. Consider the following problem in deterministic optimal control over...

Subgradient method — Class of optimization methods for nonsmooth functions. Subderivative Clarke, F. H. (1975). "Generalized gradients and applications". Transactions...

Logarithmically convex function Pseudoconvex function Quasiconvex function Subderivative of a convex function "Lecture Notes 2" (PDF). www.stat.cmu.edu. Retrieved...

semi-continuous extended real-valued functional on H. Let A stand for ∂φ, the subderivative of φ; for α > 0 let Jα denote the resolvent: J α = ( i d + α A ) − 1...

differentiable due to the kink at x = 0. Subgradient methods which rely on the subderivative can be used to solve L 1 {\displaystyle L_{1}} regularized learning...

case is the variational derivative in the calculus of variations. The subderivative and subgradient are generalizations of the derivative to convex functions...

Subgradient methods are convex optimization methods which use subderivatives. Originally developed by Naum Z. Shor and others in the 1960s and 1970s, subgradient...

convex functions by generalizing the notion of derivative to that of subderivative. Further generalization of the notion of the derivative such as the...

Wikipedia's quality standards. The specific problem is: Relationship between subderivatives and non‑convexity remains cryptic. Please help improve this section...

function f such that f(tx + (1 − t)y) ≤ max(f(x), f(y)) for t ∈ [0,1] Subderivative Geodesic convexity — convexity for functions defined on a Riemannian...