Related papers: Multiple Scale Methods For Optimization Of Discret…

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

Probabilistic learning is increasingly being tackled as an optimization problem, with gradient-based approaches as predominant methods. When modelling multivariate likelihoods, a usual but undesirable outcome is that the learned model fits…

This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…

We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of $hp$-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in…

Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Discrete energy minimization is a ubiquitous task in computer vision, yet is NP-hard in most cases. In this work we propose a multiscale framework for coping with the NP-hardness of discrete optimization. Our approach utilizes algebraic…

Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…

This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…

In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed an optimized gradient method (OGM) for this problem and…

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability…

The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…

This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…