Related papers: The Deflated Conjugate Gradient Method: Convergenc…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
Pipelined Krylov subspace methods avoid communication latency by reducing the number of global synchronization bottlenecks and by hiding global communication behind useful computational work. In exact arithmetic pipelined Krylov subspace…
The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous semi-conjugate gradient (SCG) method for unsymmetric positive definite linear systems.…
Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine…
We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
The problem of optimal precision switching for the conjugate gradient (CG) method applied to sparse linear systems is considered. A sparse matrix is defined as an $n\!\times\!n$ matrix with $m\!=\!O(n)$ nonzero entries. The algorithm first…
A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized…
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…
This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While…
We study high-probability (HP) convergence guarantees in decentralized stochastic optimization, where multiple agents collaborate to jointly train a model over a network. Existing HP results in decentralized settings almost exclusively…
Block Krylov methods have recently gained a lot of attraction. Due to their increased arithmetic intensity they offer a promising way to improve performance on modern hardware. Recently Frommer et al. presented a block Krylov framework that…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
The resolvent Krylov subspace method builds approximations to operator functions $f(A)$ times a vector $v$. For the semigroup and related operator functions, this method is proved to possess the favorable property that the convergence is…
In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace…
This paper considers the problem of multi-agent distributed optimization. In this problem, there are multiple agents in the system, and each agent only knows its local cost function. The objective for the agents is to collectively compute a…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…