Related papers: Deflation for the off-diagonal block in symmetric …
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…
With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the…
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
The global minimum point of an optimization problem is of interest in engineering fields and it is difficult to be found, especially for a nonconvex large-scale optimization problem. In this article, we consider a new memetic algorithm for…
Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of values rather than being just a fixed integer/fraction as it…
Krylov subspace methods are a ubiquitous tool for computing near-optimal rank $k$ approximations of large matrices. While "large block" Krylov methods with block size at least $k$ give the best known theoretical guarantees, block size one…
We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [2] of this work we established that agents cluster around a network…
In this paper, we study the (decentralized) distributed optimization problem with high-dimensional sparse structure. Building upon the FedDA algorithm, we propose a (Decentralized) FedDA-GT algorithm, which combines the \textbf{gradient…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…
The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…
The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains,…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…
The distributed setting for Saddle Problems (SPs) has recently emerged as a framework for various modern applications in machine learning and multiagent systems. Despite its relevance, the theoretical foundations of this setting have not…
In this paper, an efficient parallel splitting method is proposed for the optimal control problem with parabolic equation constraints. The linear finite element is used to approximate the state variable and the control variable in spatial…