Related papers: A Constructive Approach to a Class of Overdetermin…
We present a new type of modified Galerkin method. It is a construction with several (inductively defined) levels, that provides approximate solutions of increasing accuracy with every new level. These solutions are constructed as…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
We show that in a quite general framework, the parameterized optimization problem can be so perturbed as to be generically well-posed. As an application, we provide a contribution to Stechkin theory.
We solve prescribed problems for modified Schouten tensors in the conformal classes of smooth complete metrics, which extends the results obtained in prequel \cite{yuan-PUE1}. The key ingredient is to confirm the uniform ellipticity of…
We consider an overdetermined Serrin's type problem in space forms and we generalize Weinberger's proof in [Arch. Rational Mech. Anal., 43 (1971)] by introducing a suitable P-function.
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or…
A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in…
This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and…
We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's accelerated interpretation. We show that one method is…
We exhibit several counterexamples showing that the famous Serrin's symmetry result for semilinear elliptic overdetermined problems may not hold for partially overdetermined problems, that is when both Dirichlet and Neumann boundary…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
We consider the perturbed Mann's iterative process \begin{equation} x_{n+1}=(1-\theta_n)x_n+\theta_n f(x_n)+r_n, \end{equation} where $f:[0,1]\rightarrow[0,1]$ is a continuous function, $\{\theta_n\}\in [0,1]$ is a given sequence, and…
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
The present paper provides symmetry results for a class of overdetermined problems of elliptic and parabolic type in multi-phase settings, including various extensions of remarkable results obtained by S. Sakaguchi in [12, 13]. A new…
We give arguments for the existence of {\it exact} travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a…