Related papers: Linear convergence of distributed Dykstra's algori…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…

We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…

Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a…

We present two theoretical results on the computation of lambda-contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to…

We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…

The paper discusses the limitations of deep learning models in identifying and utilizing features that remain invariant under a bijective transformation on the data entries, which we refer to as combinatorial patterns. We argue that the…

We study linear regressions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often…

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…

We present an algorithm of clustering of many-dimensional objects, where only the distances between objects are used. Centers of classes are found with the aid of neuron-like procedure with lateral inhibition. The result of clustering does…

We investigate an existing distributed algorithm for learning sparse signals or data over networks. The algorithm is iterative and exchanges intermediate estimates of a sparse signal over a network. This learning strategy using exchange of…

The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and…

The paper addresses the graph classification problem and introduces a modification of the lazy associative classification method to efficiently handle intersections of graphs. Graph intersections are approximated with all common subgraphs…

In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…

A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…

We show that an almost cyclic (or generalized Gauss- Seidel) Dykstra's algorithm which incorporates the SHQP (supporting halfspace- quadratic programming) strategy can achieve nonasymptotic and asymptotic linear convergence for polyhedral…

We prove that sparse string graphs in a fixed surface have linear expansion. We extend this result to the more general setting of sparse region intersection graphs over any proper minor-closed class. The proofs are combinatorial and…

In this note we analyze two algorithms, one for producing a matching and one for an independent set, on $k$-uniform $d$-regular hypergraphs of large girth. As a result we obtain new lower bounds on the size of a maximum matching or…

We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…