相关论文: Finite Difference Approximation of Free Discontinu…
In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations
We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…
Solutions $u(x)$ to the class of inhomogeneous nonlinear ordinary differential equations taking the form \[u'' + u^2 = \alpha f(x) \] for parameter $\alpha$ are studied. The problem is defined on the $x$ line with decay of both the solution…
Tackling semi-supervised learning problems with graph-based methods has become a trend in recent years since graphs can represent all kinds of data and provide a suitable framework for studying continuum limits, e.g., of differential…
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…
We classify nontrivial, nonnegative, positively homogeneous solutions of the equation \begin{equation*} \Delta u=\gamma u^{\gamma-1} \end{equation*} in the plane. The problem is motivated by the analysis of the classical Alt-Phillips free…
This article provide new approach to solve P vs NP problem by using cardinality of bases function. About NP-Complete problems, we can divide to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…
We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…
In this paper, we study almost minimizers to a fractional Alt-Caffarelli-Friedman type functional. Our main results concern the optimal $C^{0,s}$ regularity of almost minimizers as well as the structure of the free boundary. We first prove…
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov…
We study regularity results for local minimizers of variable growth variational problem in Heisenberg groups under suitable integrability assumption on the horizontal gradient of the exponent function. More precisely, our main focus is on…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
We study the asymptotic convergence of solutions as $t\rightarrow\infty$ of $\partial_t u=-f(u)+\int f(u)$, a nonlocal differential equation that is formally a gradient flow in a constant-mass subspace of $L^2$ arising from simplified…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…