Results 181 to 190 of about 1,716 (212)

Lipschitz continuity of local minimizers of a nonconvex functional

Applicable Analysis, 1988
Lipschitz continuity of local minimizers of the energy functional of an isotropic compressible hyperelastic material is studied. The functional is a nonconvex function of the deformation gradient.
Reza Malek-madani, Penny D. Smith
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Exact penalty functions and stability in locally Lipschitz programming

Mathematical Programming, 1984
We extend the theory of exact penalty functions for nonlinear programs whose objective functions and equality and inequality constraints are locally Lipschitz; arbitrary simple constraints are also allowed. Assuming a weak stability condition, we show that for all sufficiently large penalty parameter values an isolated minimum of the nonlinear program ...
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Minimax Theorems for Locally Lipschitz Functionals and Applications

2001
The purpose of this chapter is to present several variants of minimization and mountain-pass theorems for nondifferentiable functionals. We assume that the given functionals are locally Lipschitz so that their generalized gradients can be defined (cf. Clarke [Cl] ). A general critical point theory for locally Lipschitz functionals was developed by K. C.
Maria do Rosário Grossinho, Stepan Agop Tersian   +1 more
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Another Proof that Convex Functions are Locally Lipschitz

The American Mathematical Monthly, 1974
(1974). Another Proof that Convex Functions are Locally Lipschitz. The American Mathematical Monthly: Vol. 81, No. 9, pp. 1014-1016.
A. W. Roberts, D. E. Varberg
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Concerning Differentiability Properties of Locally Lipschitz Functions

2001
Preiss proved that on an Asplund space the Clarke subdifferential of a locally Lipschitz function can be expressed in terms of its Frechet derivatives. We extend this result for the wider class of Asplund generated spaces. Zajicek examined the relation between Frechet subdifferentiability and Frechet differentiability for a locally Lipschitz function ...
J. R. Giles, Scott Sciffer
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ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds

Advances in Computational Mathematics, 2015
This paper presents a descent direction method for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we define a set-valued mapping (Formula presented.) named ε-subdifferential which is an approximation for the Clarke subdifferential and which generalizes the Goldstein- ε-subdifferential to the Riemannian ...
Philipp Grohs, Seyedehsomayeh Hosseini
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On theL 1 exact penalty function with locally lipschitz functions

Acta Mathematicae Applicatae Sinica, 1988
In this paper, we discuss the following inequality constrained optimization problem (P) minf(x) subject tog(x)⩽0,g(x)=(g1(x), ...,gr(x))τ, wheref(x),gj(x)(j=1, ...,r) are locally Lipschitz functions. TheL1 exact penalty function of the problem (P) is (PC) minf(x)+cp(x) subject tox eRn, wherep(x)=max {0,g1(x), ...,gr(x)},c>0.
Liansheng Zhang, Zhijian Huang
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Hemivariational inequalities with functionals which are not locally Lipschitz

Nonlinear Analysis: Theory, Methods & Applications, 1995
Let \(V\) be a reflexive Banach space with its dual space \(V^*\), which is imbedded in \(L^p(\Omega, R^N)\), \(1 < p < \infty\), \(N \geq 1\). Assume that \(T : V \to V^*\) is a weakly continuous operator, \(f \in V^*\) and \(j : \Omega \times R^N \to R\) is a function with the property that for almost all \(x \in \Omega\), \(\xi \to j(x,\xi)\) is ...
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A minimax theorem for locally Lipschitz functionals and applications

Journal d'Analyse Mathématique
In this paper, the authors first prove a abstract theorem which provides multiple critical points for a locally Lipschitz and even functional. This abstract theorem develops the nonsmooth critical point theory. Then, they apply the abstract theorem to find multiple solutions for the problem \[ \begin{cases} -\Delta u=f(x, u)+\mu |u|^{2^*-2}u, &\text{in}
Furtado, Marcelo F., Da Silva, João Pablo P.   +1 more
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Hemivariational Inequalities for Locally Lipschitz Functionals

2021
Z. Naniewicz, P. D. Panagiotopoulos
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