Related papers: Fej\'er monotone sequences revisited
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
Using the Markov distance and Ptolemy inequality introduced by Lee-Li-Rabideau-Schiffler \cite{LLRS}, we completely determine the monotonicity of the generalized Markov numbers along the lines of a given slope.
Recently, P\'{a}lfia introduced a generalized Karcher mean as a solution of an operator equation. In this article, we present several relations for this new mean. In particular, we investigate the behavior of this generalized mean when…
In this paper, we generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence these of sets, where $f$ is an unbounded modulus. It is shown that the Wijsman…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
For many real-life Bayesian networks, common knowledge dictates that the output established for the main variable of interest increases with higher values for the observable variables. We define two concepts of monotonicity to capture this…
In this paper, based on the Tikhonov regularization technique, we study a monotone general variational inequality (GVI) by considering an associated strongly monotone GVI, depending on a regularization parameter $\alpha,$ such that the…
We introduce a notion of variable quasi-Bregman monotone sequence which unifies the notion of variable metric quasi-Fej\'er monotone sequences and that of Bregman monotone sequences. The results are applied to analyze the asymptotic…
The performance of deep neural networks is often attributed to their automated, task-related feature construction. It remains an open question, though, why this leads to solutions with good generalization, even in cases where the number of…
Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…
The dominated convergence theorem implies that if (f_n) is a sequence of functions on a probability space taking values in the interval [0,1], and (f_n) converges pointwise a.e., then the sequence of integrals converges to the integral of…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
In federated optimization, heterogeneity in the clients' local datasets and computation speeds results in large variations in the number of local updates performed by each client in each communication round. Naive weighted aggregation of…
We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…
In this paper, we consider the well known problem of estimating a density function under qualitative assumptions. More precisely, we estimate monotone non increasing densities in a Bayesian setting and derive concentration rate for the…
The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context…
This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…
We consider a uniqueness problem concerning the Fourier coefficients of normalized Cauchy transforms. These problems inherently involve proving a simultaneous approximation phenomenon and establishing the existence of cyclic inner functions…
In the preprint of 1993 the author formulated some conjectures on monotonicity of ratios for exponential series remainders. They are equivalent to conjectures on monotonicity of a ratio of Kummer hypergeometric functions and presumably not…
In this dissertation, we show that the Central Limit Theorem and the Invariance Principle for Discrete Fourier Transforms discovered by Peligrad and Wu can be extended to the quenched setting. We show that the random normalization…