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Concept

Master theorem

Publications associées (12)

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Mehmet Fatih Sahin

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

EPFL2023

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

Paths in pseudorandom graphs and applications

Van Thang Pham

Let G = (V, E) be an (n, d, lambda)-graph. In this paper, we give an asymptotically tight condition on the size of U subset of V such that the number of paths of length k in U is close to the expected number for arbitrary integer k >= 1. More precisely, we ...

CHARLES BABBAGE RES CTR2020

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Daniel Kressner, Stefano Massei

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

SIAM PUBLICATIONS2019

An adaptive primal-dual framework for nonsmooth convex minimization

Volkan Cevher, Quoc Tran Dinh, Ahmet Alacaoglu

We propose a new self-adaptive and double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov’s smoothing technique via general Bregman distance functions. It self-adaptiv ...

2020

Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization

Jan Sickmann Hesthaven, Paolo Gatto

We previously introduced a preconditioner that has proven effective for hp-FEM dis- cretizations of various challenging elliptic and hyperbolic problems. The construc- tion is inspired by standard nested dissection, and relies on the assumption that the Sc ...

Elsevier2017

Constrained LQR Using Online Decomposition Techniques

Colin Neil Jones, Georgios Stathopoulos

This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without ...

2016

An Algorithmic Framework for Mumford-Shah Regularization of Inverse Problems in Imaging

Martin Kurt Storath

The Mumford-Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this pap ...

Iop Publishing Ltd2015

Path-following gradient-based decomposition algorithms for separable convex optimization

Quoc Tran Dinh

A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require ...

Springer Verlag2014

Cracking The Complexity Of Fixed-Point Refinement In Complex Wireless Systems

Paolo Ienne, David Novo Bruna

Fixed-point arithmetic leads to efficient implementations. However, the optimization process required to size each of the implementation signals can be prohibitively complex. In this paper, we introduce a new divide-and-conquer method that is able to appro ...

Ieee2013

Container Terminal Management : Integrated Models and Large-Scale Optimization Algorithms

Ilaria Vacca

This thesis deals with models and methods for large scale optimization problems; in particular, we focus on decision problems arising in the context of seaport container terminals for the efficient management of terminal operations. Large-scale optimizatio ...

EPFL2011

A Divide-and-Conquer Approach for Solving Interval Algebra Networks

Jingshi Li

Deciding consistency of constraint networks is a fundamental problem in qualitative spatial and temporal reasoning. In this paper we introduce a divide-and-conquer method that recursively partitions a given problem into smaller sub-problems in deciding con ...

2009