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An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…
Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…
In the theory of linear switching systems with discrete time, as in other areas of mathematics, the problem of studying the growth rate of the norms of all possible matrix products $A_{\sigma_{n}}\cdots A_{\sigma_{0}}$ with factors from a…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
We present a framework based on multiple Lyapunov functions to find probabilistic data-driven guarantees on the stability of unknown constrained switching linear systems (CSLS), which are switching linear systems whose switching signal is…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active…
In this work, a wide family of LFSR-based sequence generators, the so-called Clock-Controlled Shrinking Generators (CCSGs), has been analyzed and identified with a subset of linear Cellular Automata (CA). In fact, a pair of linear models…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of $n\times n$ matrices and an $n$-dimensional vector, find a sequence of $K$ matrices, each chosen from the…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…
This paper presents algorithms for identifying and reducing a dedicated set of controllable transition rates of a state-labelled continuous-time Markov chain model. The purpose of the reduction is to make states to satisfy a given…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…