subderivatives (or subgradient) generalizes the derivative to convex functions which are not necessarily differentiable. The set of subderivatives at...
8 KB (1,269 words) - 13:54, 28 September 2024
many subderivatives at zero, with just one of them taking the value sgn ( 0 ) = 0 {\displaystyle \operatorname {sgn}(0)=0} . A subderivative value...
16 KB (2,784 words) - 10:57, 23 September 2024
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...
29 KB (4,617 words) - 16:05, 21 October 2024
Convex function Invex function Legendre transformation Semi-continuity Subderivative Main results (list) Carathéodory's theorem Ekeland's variational principle...
61 KB (7,161 words) - 05:35, 2 November 2024
for problems of differential equations and in functional analysis. Subderivative Weyl's lemma (Laplace equation) Gilbarg, D.; Trudinger, N. (2001). Elliptic...
7 KB (1,021 words) - 09:04, 8 May 2024
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...
30 KB (4,619 words) - 15:58, 5 November 2024
Subgradient method — Class of optimization methods for nonsmooth functions. Subderivative Clarke, F. H. (1975). "Generalized gradients and applications". Transactions...
3 KB (392 words) - 12:45, 28 September 2024
Logarithmically convex function Pseudoconvex function Quasiconvex function Subderivative of a convex function "Lecture Notes 2" (PDF). www.stat.cmu.edu. Retrieved...
35 KB (5,852 words) - 07:11, 5 September 2024
required, in which conventional derivatives are replaced by (set-valued) subderivatives. Consider the following problem in deterministic optimal control over...
14 KB (2,050 words) - 17:50, 26 April 2024
{\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...
27 KB (3,966 words) - 08:11, 14 June 2024