Related papers: On Lipschitzian properties of multifunctions defin…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called…
The subject of the present paper are stability properties of the solution set to set-valued inclusions. The latter are problems emerging in robust optimization and mathematical economics, which can not be cast in traditional generalized…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric…
We prove the existence of density for the solution to the multiplicative semilinear stochastic heat equation on an unbounded spatial domain, with drift term satisfying a half-Lipschitz type condition. The methodology is based on a careful…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated by a conceptually simple observation: every Lipschitz…
In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior which is uniformly Lipschitz and…
This work concerns the study of the subdifferential of the integral functional $$ E_f(x)=\int_{T} f(t,x)d\mu(t), $$ where $f$ is a (not necessarily convex) normal integrand, $({T},\mathcal{A},\mu)$ is a $\sigma$-finite measure space, while…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
We consider a semilinear elliptic equation with a nonsmooth, locally \hbox{Lipschitz} potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our…
The paper investigates the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities in families of ideals. It is shown that Hilbert-Samuel multiplicity is upper semicontinuous almost generally and that Hilbert-Kunz multiplicity is upper…
In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
The starting assumptions to study the convergence and complexity of gradient-type methods may be the smoothness (also called Lipschitz continuity of gradient) and the strong convexity. In this note, we revisit these two basic properties…