Related papers: A-priori error analysis of local incremental minim…
This paper is concerned with an approximation scheme for rate-independent systems governed by a non-smooth dissipation and a possibly non-convex energy functional. The scheme is based on the local minimization scheme introduced in [EM06],…
We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) non-convex energy and a dissipation potential, which is positively homogeneous of…
It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
We derive an implicit numerical scheme for the solution of advection equation where the roles of space and time variables are exchanged using the inverse Lax-Wendroff procedure. The scheme contains a linear weight for which it is always…
Minibatch decomposition methods for empirical risk minimization are commonly analysed in a stochastic approximation setting, also known as sampling with replacement. On the other hands modern implementations of such techniques are…
In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…
A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
We provide for first order discretizations of the integral fractional Laplacian sharp local error estimates on proper subdomains in both the local $H^1$-norm and the localized energy norm. Our estimates have the form of a local best…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we…
We consider the discretization of parabolic initial boundary value problems by finite element methods in space and a Runge-Kutta time stepping scheme. Order optimal a-priori error estimates are derived in an energy-norm under natural…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…