Sentence examples for a proximity operator from inspiring English sources

where prox is a proximity operator.

In order to solve ℓ 1 norm, the soft threshold function as a proximity operator is usually used, which is mathrm{soft}left(mathbf{v},tau right)=mathit{operatorname{sign}}left(mathbf{v}right)otimes max left{left|mathbf{v}right|-tau, 0right} (24).

The parallel algorithm does not use any proximity operators, in contrast to conventional parallel algorithms.

The proposed algorithm does not use any proximity operators, in contrast to conventional parallel algorithms for nonsmooth convex optimization.

In fact, the proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set.

We study the construction of the proximity operator of a perspective function under general assumptions and present important instances in which the proximity operator can be computed explicitly or via straightforward numerical operations.

It is easy to see that (operatorname{prox}_{gammachi_{C}}= operatorname{proj}_{C}) for all (gamma>0), and the proximity operator is a generalization of projection operator.

We first give an explicit form for the proximity operator (text {prox}_{frac {1}{beta }iota _{mathcal {C}}}).

Here (operatorname{prox}_{f}) is the proximity operator [21] of a function f; see (2.2).

If we would have a closed-form expression for such proximity operator or if we could approximate it efficiently (with the approximation errors decreasing at appropriate rates [27]), then we could efficiently solve (7).

Now, with the help of the subdifferential and the proximity operator, we can characterize a solution of the indicator function based on model (2) via fixed-point equations.