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A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
We study local regularity properties of local minimizer of scalar integral functionals of the form $$\mathcal F[u]:=\int_\Omega F(\nabla u)-f u\,dx$$ where the convex integrand $F$ satisfies controlled $(p,q)$-growth conditions. We…
A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It depends on the existence of two positive definite weight…
PI controllers are the most widespread type of controllers and there is an intuitive understanding that if their gains are sufficiently small and of the correct sign, then they always work. In this paper we try to give some rigorous backing…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
Two local discontinuous Galerkin (LDG) methods using some non-standard numerical fluxes are developed for the Helmholtz equation with the first order absorbing boundary condition in the high frequency regime. It is shown that the proposed…
Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance. Despite extensive development of convergence guarantees under various assumptions in recent years, most require the Lipschitz…
This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications…
We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…
For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
We introduce a notion of "local stability in permutations" for finitely generated groups. If a group is sofic and locally stable in our sense, then it is also locally embeddable into finite groups (LEF). Our notion is weaker than the…
In many real-world applications, it is undesirable to drastically change the problem solution after a small perturbation in the input, as unstable outputs can lead to costly transaction fees, privacy and security concerns, reduced user…
We provide a new understanding of the stochastic gradient bandit algorithm by showing that it converges to a globally optimal policy almost surely using \emph{any} constant learning rate. This result demonstrates that the stochastic…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
We consider the problem of computing the closest stable/unstable non-negative matrix to a given real matrix. This problem is important in the study of linear dynamical systems, numerical methods, etc. The distance between matrices is…
The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal additive…
The small-signal stability is an integral part of the power system security analysis. The introduction of renewable source related uncertainties is making the stability assessment difficult as the equilibrium point is varying rapidly. This…
The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been…