Related papers: Factorization of Saddle-point Matrices in Dynamica…

Federated learning (FL) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean…

Although many real-world stochastic planning problems are more naturally formulated by hybrid models with both discrete and continuous variables, current state-of-the-art methods cannot adequately address these problems. We present the…

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

Data sparsity has been one of the long-standing problems for recommender systems. One of the solutions to mitigate this issue is to exploit knowledge available in other source domains. However, many cross-domain recommender systems…

Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…

This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…

The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…

This paper proposes and analyzes an iterative minimization formulation for search- ing index-1 saddle points of an energy function. This formulation differs from other eigenvector-following methods by constructing a new objective function…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

A \emph{saddlepoint} of an $n \times n$ matrix is an entry that is the maximum of its row and the minimum of its column. Saddlepoints give the \emph{value} of a two-player zero-sum game, corresponding to its pure-strategy Nash equilibria;…

For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data…

Recently, data-enabled predictive control (DeePC) schemes based on Willems' fundamental lemma have attracted considerable attention. At the core are computations using Hankel-like matrices and their connection to the concept of persistency…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

This work investigates diagonalization-based methods for efficiently solving linear evolution problems, with a particular focus on the heat equation. The plain diagonalization of the differential operator, though effective for elliptic…

We solve large-scale mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This is motivated by the MILPs being able to model problems in multi-agent autonomy, e.g., task assignment problems and…

We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that…

Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…

Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…

We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…