- differentiable. The set of
subderivatives at a
point is
called the
subdifferential at that point.
Subderivatives arise in
convex analysis, the
study of...
-
respect to z {\displaystyle z} for all x {\displaystyle x} , then the
subdifferential of f ( x ) {\displaystyle f(x)} is
given by ∂ f ( x ) = c o n v { ∂...
- (x)}{\theta }},} is
decreasing as θ
approaches 0+. In particular, the
subdifferential of φ {\displaystyle \varphi }
evaluated at x in the
direction y is...
- f:X\to [-\infty ,\infty ]} and x ∈ X {\displaystyle x\in X} then the
subdifferential set is ∂ f ( x ) : = { x ∗ ∈ X ∗ : f ( z ) ≥ f ( x ) + ⟨ x ∗ ,...
- point,
including at the origin.
Everywhere except zero, the
resulting subdifferential consists of a
single value,
equal to the
value of the sign function...
-
solution to be optimal. If some of the
functions are non-differentiable,
subdifferential versions of Karush–Kuhn–Tucker (KKT)
conditions are available. Under...
- f} .
Since the
subdifferential of a proper, convex,
lower semicontinuous function on a
Hilbert space is
inverse to the
subdifferential of its
convex conjugate...
-
achieves a
global minimum where the
derivative does not exist. The
subdifferential of |x| at x = 0 is the interval [−1, 1]. The
complex absolute value...
- is positive. More precisely, this is
characterized in
terms of the
subdifferential ∂ f {\displaystyle \partial f} as follows: For all x , y ∈ X {\displaystyle...
- x-p\in \partial f(p)} ,
where ∂ f {\displaystyle \partial f} is the
subdifferential of f {\displaystyle f} ,
given by ∂ f ( x ) = { u ∈ R N ∣ ∀ y ∈ R N...
