Related papers: Subgradients of Minimal Time Functions without Cal…
This paper concerns the study of a broad class of minimal time functions corresponding to control problems with constant convex dynamics and closed target sets in arbitrary Banach spaces. In contrast to other publications, we do not impose…
The paper is devoted to the classical variational problem with a nonsmooth integrand of the functional to be minimized. The integrand is supposed to be subdifferentiable. Under some natural conditions the subdifferentiability of the…
In this paper we first consider the class of minimal time functions in the general setting of locally convex topological vector (LCTV) spaces. The results obtained in this framework are based on a novel notion of closedness of target sets…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
In this paper, we provide a number of subdifferential formulas for a class of nonconvex infimal convolutions in normed spaces. The formulas obtained unify several results on subdifferentials of the distance function and the minimal time…
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation…
In this paper, we revisit the Mordukhovich's subdifferential criterion for Lipschitz continuity of nonsmooth functions and coderivative criterion for the Aubin/Lipschitz-like property of set-valued mappings in finite dimensions. The…
This paper investigates some aspects of the variational behaviour of nonsmooth functions, with special emphasis on certain stability phenomena. Relationships linking such properties as sharp minimality, superstability, error bound and…
We show that all non-negative submodular functions have high {\em noise-stability}. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on $\{-1,1\}^n$ (for any constant…
We show that the subgradient method converges only to local minimizers when applied to generic Lipschitz continuous and subdifferentially regular functions that are definable in an o-minimal structure. At a high level, the argument we…
Subdifferentials (in the sense of convex analysis) of matrix-valued functions defined on $\mathbb{R}^d$ that are convex with respect to the L\"{o}wner partial order can have a complicated structure and might be very difficult to compute…
To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…
Over the past decades, the concept "partial smoothness" has been playing as a powerful tool in several fields involving nonsmooth analysis, such as nonsmooth optimization, inverse problems and operation research, etc. The essence of partial…
The paper studies generalized differentiability properties of the marginal function of parametric optimal control problems of semilinear elliptic partial differential equations. We establish upper estimates for the regular and the limiting…
We establish general assumptions under which a constrained vari- ational problem involving the fractional gradient and a local nonlin- earity admits minimizers.
This work provides calculus for the Fr\'echet and limiting subdifferential of the pointwise supremum given by an arbitrary family of lower semicontinuous functions. We start our study showing fuzzy results about the Fr\'echet…
In this paper we consider the question of smoothness of slowly varying functions satisfying the modern definition that, in the last two decades, gained prevalence in the applications concerning function spaces and interpolation. We show,…
The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…
We collect here some known results on the subdifferential of one-homogeneous functionals, which are anisotropic and nonhomogeneous variants of the total variation and establish a new relationship between Lebesgue points of the calibrating…