Related papers: Structure, Analysis, and Synthesis of First-Order …
Optimization underpins many of the challenges that science and technology face on a daily basis. Recent years have witnessed a major shift from traditional optimization paradigms grounded on batch algorithms for medium-scale problems to…
This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or partially known. In particular, we focus on the design of data-driven…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
Most algorithms for decentralized learning employ a consensus or diffusion mechanism to drive agents to a common solution of a global optimization problem. Generally this takes the form of linear averaging, at a rate of contraction…
We discuss a dynamical systems perspective on discrete optimization. Departing from the fact that many combinatorial optimization problems can be reformulated as finding low energy spin configurations in corresponding Ising models, we…
We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…
Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when using optimizers relying only on local information, such as SGD. Indeed, this was a primary source of…
This article seeks to contribute to a nuanced understanding of the integration of Design Structure Matrix (DSM) and genetic algorithms in the context of Complex Systems modelling described within Model-Based System Engineering approach. By…
In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
In this paper, we consider networked systems comprised of interconnected sets of linear subsystems and propose a decentralized and compositional approach to stabilize or dissipativate such linear networked systems via optimally modifying…
This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…
This paper addresses data-driven control of continuous-time systems. We develop a framework based on synthesis operators associated with input and state trajectories. A key advantage of the proposed method is that it does not require the…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
The convergence rate of various first-order optimization algorithms is a pivotal concern within the numerical optimization community, as it directly reflects the efficiency of these algorithms across different optimization problems. Our…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…