Related papers: Optimal Krylov On Average
Model-based reconstruction plays a key role in compressed sensing (CS) MRI, as it incorporates effective image regularizers to improve the quality of reconstruction. The Plug-and-Play and Regularization-by-Denoising frameworks leverage…
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…
In this paper, we study the distributed nonconvex optimization problem, which aims to minimize the average value of the local nonconvex cost functions using local information exchange. To reduce the communication overhead, we introduce…
This paper considers time-average optimization, where a decision vector is chosen every time step within a (possibly non-convex) set, and the goal is to minimize a convex function of the time averages subject to convex constraints on these…
We propose a fast collocation method based on Krylov subspace iterative solver on general nonuniform grids for the fractional Laplacian problem, in which the fractional operator is presented in a singular integral formulation. The method is…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method.…
This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using multi-agents with Markov switched network dynamics and noisy inter-agent communications. Unlike…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
In this paper, we present a novel derivative-free optimization framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning involve settings…
In this paper, we apply acceleration to the inverse-free preconditioned Krylov subspace method introduced by Golub and Ye, which solves the symmetric generalized eigenvalue problem for the algebraically smallest eigenvalue. As the method is…
In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…
To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…
Practical online learning tasks are often naturally defined on unconstrained domains, where optimal algorithms for general convex losses are characterized by the notion of comparator adaptivity. In this paper, we design such algorithms in…
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…
New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…
A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral…
In this paper we consider a constrained parabolic optimal control problem. The cost functional is quadratic and it combines the distance of the trajectory of the system from the desired evolution profile together with the cost of a control.…
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…
We propose a flexible gradient tracking approach with adjustable computation and communication steps for solving distributed stochastic optimization problem over networks. The proposed method allows each node to perform multiple local…