Symmetry in systems arises as a result of natural design and provides pivotal mechanism for crucial system properties. In the field control theory, scattered research has been carried out concerning group-theoretic symmetric systems. this manuscript, principles stochastic analysis, fixed-point theorem, fractional calculus, multivalued map theory are implemented to investigate null boundary cont...

In this paper we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke-Rockafellar subdifferential. Further we extend to programs with pseudoconvex objective function two earlier characterizations of the solutions set of a set constrained nonlinear programming problem due to O...

In this paper, we generalize the extended supporting hyperplane algorithm for a convex continuously differentiable mixed-integer nonlinear programming problem to solve a wider class of nonsmooth problems. The generalization is made by using the subgradients of the Clarke subdifferential instead of gradients. Consequently, all the functions in the problems are assumed to be locally Lipschitz con...

In this paper, we study a dynamic contact problem with Clarke subdifferential boundary conditions. The material is assumed to be viscoplastic which has an implicit expression of the stress field in constitutive law. weak form model governed by evolutionary hemivariational inequality coupled integral equation. We fully discrete approximation scheme and bound errors. Under appropriate solution re...

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law materials has an implicit expression stress field, weak form is evolutionary hemivariational inequality coupled integral equation. By providing some equivalent formulati...

Abstract In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential condition on portion described by Clarke generalized gradient locally Lipschitz function. First, prove new existence result for inequality employing theory pseudomonotone operators. Next, give comparis...

This paper presents an extension of stochastic gradient descent for the minimization Lipschitz continuous loss functions. Our motivation is use in non-smooth non-convex optimization problems, which are frequently encountered applications such as machine learning. Using Clarke $$\epsilon $$ -subdifferential, we prove non-asymptotic convergence to approximate stationary point expectation proposed...

We present a survey on the results related to the theory of lexicographic differentiation. This theory ensures an efficient computation of generalized (lexicographic) derivative of a nonsmooth function belonging to a special class of lexicographically smooth functions. This class is a linear space which contains all differentiable functions, all convex functions, and which is closed with respec...

The Mordukhovich subdifferential, being highly important in variational and non-smooth analysis and optimization, often happens to be hard to calculate. We propose a method for computing the Mordukhovich subdifferential of differences of sublinear (DS) functions via the directed subdifferential of differences of convex (DC) functions. We restrict ourselves to the two-dimensional case mainly for...