Sentence examples for because the nonsmooth function from inspiring English sources

These methods are also called proximal splitting because the nonsmooth function is involved via its proximity operator.

The nonsmooth function is approximated by a smooth operator.

On the other hand, we generalize the method of [13] from minimizing a single nonconvex nonsmooth function to the sum of two functions.

Additionally, the nonsmooth objective function precludes the use of rapidly converging derivative-based optimization algorithms.

where F B ( B ) = 1 2 ∥ A BC t-1 ) − Y ∥ F 2 + 1 2 ∥ C t-1 ∥ F 2. This is a composite convex optimization problem involving the sum of a smooth function (F B (B)) and a nonsmooth function (λ∥B∥2,1).

However, in many applications, the max norm of tracking error is critical, which is a nonsmooth function and thus gradient-based ILC methods cannot be directly used.

Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function.

Let and be a nonsmooth function.

The incremental subgradient method ([24], Section 8.2) and the projected multi-agent algorithms [25 28] can minimize the sum of nonsmooth, convex functions over a simple constraint set by using the subgradients ([29], Section 23) of the nonsmooth, convex functions instead of the proximity operators.

The proposed PDFP algorithm is a symmetric and fully splitting scheme, only involving explicit gradient and linear operators without any inversion and subproblem solving, when the proximity operator of nonsmooth functions can easily be handled.

Proximal Newton-type methods for minimizing composite functions (unconstrained optimization of the sum of smooth and nonsmooth functions) (Matlab).