Related papers: Generalized Differentiation and Characterizations …
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…
This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field R^{*}\supset R. They have been introduced and studied in some previous works ([1],[2],[3]). In this paper we introduce a modified notion of ultrafunction…
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…
These lecture notes for a graduate course cover generalized derivative concepts useful in deriving necessary optimality conditions and numerical algorithms for nondifferentiable optimization problems in inverse problems, imaging, and…
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older…
In calculus, an indefinite integral of a function $f$ is a differentiable function $F$ whose derivative is equal to $f$. In present paper, we generalize this notion of the indefinite integral from the ring of real functions to any ring. The…