Related papers: On computing fixpoints in well-structured regular …

Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…

In this paper, we consider a wider class of simulation functions and present some coincidence and common fixed point results in metric spaces. Results obtained in this paper extend, generalize and unify some well-known fixed and common…

This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…

To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century when Carl Friedrich Gauss developed the…

We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular,…

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

This paper investigates the consensus problem in almost sure sense for uncertain multi-agent systems with noises and fixed topology. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the…

A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically…

We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…

This paper deals with the optimal control of systems governed by nonlinear systems of conservation laws at junctions. The applications considered range from gas compressors in pipelines to open channels management. The existence of an…

Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…

We prove a centre manifold theorem for a map along a manifold-with-boundary of fixed points, and provide an application to the study of gradient descent with large step size on two-layer matrix factorisation problems.

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…

In his recent research M. K. Tam (2018) considered a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator. At each point in the ambient space, the value of the operator can…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

The RFMP is an iterative regularization method for a class of linear inverse problems. It has proved to be applicable to problems which occur, for example, in the geosciences. In the early publications [Fischer2011] and [FischerMichel2012],…

The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…

Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.…