Related papers: Convergence of difference inclusions via a diamete…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
This paper concerns with mesh restrictions that are needed to satisfy several important mathematical properties -- maximum principles, comparison principles, and the non-negative constraint -- for a general linear second-order elliptic…
Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely unexplored. In this paper we study SGD with increasing…
The evolution of local defects such as dislocations and cracks often determines the performance of engineering materials. For a proper description and understanding of these phenomena, one needs to descend to a very small scale, at which…
We investigate convergence properties of a proposed distributed model predictive control (DMPC) scheme, where agents negotiate to compute an optimal consensus point using an incremental subgradient method based on primal decomposition as…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
The importance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations.…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
The framework of Integral Quadratic Constraints (IQCs) is used to perform an analysis of gradient descent with varying step sizes. Two performance metrics are considered: convergence rate and noise amplification. We assume that the step…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…
An empirical investigation of the interaction of sample size and discretization - in this case the entropy-based method CAIM (Class-Attribute Interdependence Maximization) - was undertaken to evaluate the impact and potential bias…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or…
We examine gradient descent in matrix factorization and show that under large step sizes the parameter space develops a fractal structure. We derive the exact critical step size for convergence in scalar-vector factorization and show that…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…