In this paper we prove the principle of symmetric criticality for Motreanu–Panagiotopoulos type functionals, i.e., for convex, proper, lower semicontinuous functionals which are perturbed by a locally Lipschitz function. By means of this principle a variational–hemivariational inequality is studied on certain type of unbounded strips. © 2006 Elsevier Inc. All rights reserved.

In this paper, we introduce locally Lipschitz observation systems for nonlinear semigroups and show that they can be represented by an ‘admissible’ nonlinear output operator defined on a suitable subspace. In the semilinear case, this concept fits well to the Lebesgue extension known from linear system theory. Also in the semilinear case, we show robustness of exact observability near equilibri...

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We de ne two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementati...

To each function f of bounded quadratic variation we associate a Hausdorff measure μf . We show that the map f → μf is locally Lipschitz and onto the positive cone of M[0, 1]. We use the measures {μf : f ∈ V2} to determine the structure of the subspaces of V 0 2 which either contain c0 or the square stopping time space S2.

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient soluti...

Consider the ordinary diierential equation _ xt = F , x t ; x 0 = x 0 : 1 A solution 1 on 0; T , T T 0, to 1 is a continuously diierentiable function x : : 0 ; T !R n satisfying xt = x 0 + Z t 0 F , x s ds: We m a y ask for which functions F there exist a solution to 1 and, if so, if the solution is unique. Is it, for instance, suucient that F is a continuous function? The answer is no concerni...

In this paper we address some of the most fundamental questions regarding the diierentiability structure of locally Lipschitz functions deened on Banach spaces. For example, we examine the relationship between inte-grability, D-representability and strict diierentiability. In addition to this, we show that on a large class of Banach spaces there is a signiicant family of locally Lipschitz funct...

In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability, D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipsc...

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as sum continuously differentiable convex function whose gradient is Lipschitz continuous proper lower semicontinuous (possibly nonconvex) function, denominator weakly over constraint set. This model problem includes composite optimization problems studied extensively late...