Sentence examples for methods for nonsmooth from inspiring English sources

This result is useful in designing Newton's methods for nonsmooth equations.

Recently, locally high-order convergent Newton methods for nonsmooth equations have been well established via the concept of semismoothness.

Nitish received his PhD from Northwestern University in 2017 where he worked on second-order methods for nonsmooth and stochastic optimization.

But, in order to establish more general applications of our method, it should be necessary to consider the methods for nonsmooth problems such as in [15].

In this work, we present a semi-supervised support vector classifier that is designed using quasi-Newton method for nonsmooth convex functions.

Bonettini et al. establish the convergence of a general primal-dual method for nonsmooth convex optimization problems, whose structure is typical in the imaging framework [13].

However, just as the statement in [27], a globalization of the semismooth Newton method for nonsmooth equations is very hard because the corresponding merit function is nondifferentiable in most cases.

Bonettini and Ruggiero [6] established the convergence of a general primal-dual method for nonsmooth convex optimization problems and showed that the convergence of the scheme can be considered as an ϵ-subgradient method on the primal formulation of the variational problem when the steplength parameters are a priori selected sequences.

Here P I ≡ ( ( f ( U ), ϕ i ) ) i ∈ I. System (4.4) is in fact a bilinear system of equations whose right-hand side consists of intervals with constraint conditions z I Γ ≥ 0 and w I Γ ≥ 0. To solve the nonlinear system (4.4) with automatic verification of the correctness of the result, a verification method for nonsmooth equations by a generalized Krawczyk operator as in [15] could be used.

When the constraint set of the variational inequality problem is a rectangle, several locally convergent Newton methods for the reformulated nonsmooth equations can also be globalized.

Another approach is to try to solve the nonsmooth problem directly, using general nonsmooth optimization methods, for instance, the subgradient method [17].