In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

As a representative example of a C continuous system, a four-dimensional model of the dive-plane dynamics of the supercavitating body shown in Figure 1 is considered. This model includes a dominant, nonsmooth nonlinearity associated with the planing force [1,2]. The original non-smooth system is approximated by a smooth counterpart, and it is examined as to how well the smooth system captures t...

Pseudo-transient continuation is a Newton-like iterative method for computing steady-state solutions of differential equations in cases where the initial data is far from a steady state. The iteration mimics a temporal integration scheme, with the time step being increased as steady state is approached. The iteration is an inexact Newton iteration in the terminal phase. In this paper we show ho...

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent nonsmooth Newton methods for nonsmooth equations have been well established via the concept of semismoothness. In this paper, we focus our discussions on a way of globalizing nonsmooth Newton methods based on a smoothing-nonsmooth reformulation of nonsm...

In this paper, we study quasilinear parabolic equations with the nonlinearity structure modeled after p(x, t)-Laplacian on nonsmooth domains. The main goal is to obtain end point Calderón-Zygmund type estimates in variable exponent setting. a recent work [1], obtained were strictly above natural t) and hence there was gap between energy (see (1.3) (1.2)). Here, bridge case of [1]. To end, make ...

This work presents a novel modeling paradigm of the dynamical negotiation between clients running TCP (Transmission Control Protocol) and routers with the RED (Random Early Detection) active queue management scheme. The basic aim of the modeling is to understand the inherent nonlinearity in the interaction and how it manifests itself in the parametric sensitivities observed in practice. The mod...

In this paper, efficient algorithms for contact problems with Tresca and Coulomb friction in three dimensions are presented and analyzed. The numerical approximation is based on mortar methods for nonconforming meshes with dual Lagrange multipliers. Using a nonsmooth complementarity function for the three-dimensional friction conditions, a primal-dual active set algorithm is derived. The method...

In this paper, efficient algorithms for contact problems with Tresca and Coulomb friction in three dimensions are presented and analyzed. The numerical approximation is based on mortar methods for nonconforming meshes with dual Lagrange multipliers. Using a nonsmooth complementarity function for the 3D friction conditions, a primal-dual active set algorithm is derived. The method determines act...

Total Variation-based regularization, well established for image processing applications such as denoising, was recently introduced for Maximum Penalized Likelihood Estimation (MPLE) as an effective way to estimate nonsmooth probability densities. While the estimates show promise for a variety of applications, the nonlinearity of the regularization leads to computational challenges, especially ...