Results 141 to 150 of about 231 (170)

Subdifferential Regularity of Directionally Lipschitzian Functions

Canadian Mathematical Bulletin, 2000
AbstractFormulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian.
Bounkhel, M., Thibault, L.
openaire   +2 more sources

Subgradient of distance functions with applications to Lipschitzian stability

Mathematical Programming, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boris S. Mordukhovich, Nguyen Mau Nam
openaire   +2 more sources

Solution of monotone complementarity problems with locally Lipschitzian functions

Mathematical Programming, 1997
The paper deals with complementarity problems CP(F), where the underlying function F is assumed to be locally Lipschitzian. Based on a special equivalent reformulation of CP(F) as a system of equations (Phi)(x) = 0 or as the problem of minimizing the merit function (psi) =1/2 ^ 2_2, we extend results which hold for sufficiently smooth functions F to ...
Andreas Fischer
exaly   +3 more sources

Uniformly Lipschitzian mappings in modular function spaces [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2001
Plan Andaluz de Investigación (Junta de Andalucía)
M A Khamsi, T Dominguez Benavides
exaly   +4 more sources

Isolated zeros of lipschitzian metrically regular -Functions

Optimization, 2001
Given a metrically regular locally Lipschitzian function sending $_{ℝn}$ into $_{ℝm}$,the structure of the preimages will be studied. In particular, for the case of m =n, it will be shown that all preimages are locally finite sets provided that the Lipschitzian function in question is directionally differentiable. Some consequences of this fact will be
exaly   +3 more sources

Some brief observations in minimizing the sum of locally Lipschitzian functions

Optimization Letters, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wim Van Ackooij, Welington De Oliveira, De Oliveira Welington   +2 more
exaly   +4 more sources

Dini Derivatives of the Marginal Function of a Non-Lipschitzian Program

SIAM Journal on Optimization, 1996
Summary: Upper and lower bounds are establised for the Dini directional derivatives of the marginal function of a parametric mathematical program. In this program, the equality constraint functions are assumed to be strictly differentiable, but the objective and inequality constraint functions can belong to a large class of non-Lipschitzian functions ...
openaire   +2 more sources

Lipschitzian semigroups and abstract functional differential equations

Nonlinear Analysis: Theory, Methods & Applications, 2010
The authors consider the abstract functional differential equation \[ (FDE)\quad u'(t)=Au(t)+\Phi u_t, \quad t>0,\quad u(0)=x,\quad u_0=f, \] where \(A\) is a closed and densely defined linear operator, \(\Phi:L^p([-1,0];X)\to X\) is a globally Lipschitz operator, \(f\in L^p([-1,0];X)\) and \(u_t(\sigma):=u(t+\sigma)\). By assuming that the space \(X\)
Song, Xueli, Peng, Jigen
openaire   +2 more sources

The Lipschitzianity of convex vector and set-valued functions

TOP, 2015
Let \(X,Y\) be normed spaces and \(C\) a proper convex cone in \(Y\) inducing an order relation \(\leq_C\) on \(Y\). One puts \(Y^\bullet=Y\cup\{+\infty\}\), where \(+\infty\) is an ideal element attached to \(Y\) such that \(y\leq_C+\infty\) for all \(y\in Y\). The \(C\)-convexity of a function \(f:X\to Y^\bullet\) is defined in the usual way by using
Vu Anh Tuan, Tammer, Christiane, Zălinescu, Constantin   +2 more
openaire   +2 more sources

A Global Optimization Algorithm for Multivariate Functions with Lipschitzian First Derivatives

Journal of Global Optimization, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources