Sentence examples for method for nonsmooth from inspiring English sources

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].

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

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.

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.

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 paper, we propose a method for smoothing the nonsmooth lower-order exact penalty function for inequality constrained optimization.

In this paper, we propose a new generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions.

The investigation focuses on the use of semismooth inexact Newton method for the case with nonsmooth topography and the use of two- and three-level overlapping Schwarz methods with different order of discretizations for the preconditioning of the Jacobian systems.