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We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…
High-velocity streams of high-dimensional data pose significant "big data" analysis challenges across a range of applications and settings. Online learning and online convex programming play a significant role in the rapid recovery of…
We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…
In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown $d$-dimensional parameter, which might be subject to Gaussian random noises. The sensors…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they…
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…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
Distributed Optimization is an increasingly important subject area with the rise of multi-agent control and optimization. We consider a decentralized stochastic optimization problem where the agents on a graph aim to asynchronously optimize…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…
Dynamic networks consist of a sequence of time-varying networks, and it is of great importance to detect the network change points. Most existing methods focus on detecting abrupt change points, necessitating the assumption that the…
In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…
Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where…
We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
Homography estimation between multiple aerial images can provide relative pose estimation for collaborative autonomous exploration and monitoring. The usage on a robotic system requires a fast and robust homography estimation algorithm. In…
We present a new method for minimizing the sum of a differentiable convex function and an $\ell_1$-norm regularizer. The main features of the new method include: $(i)$ an evolving set of indices corresponding to variables that are predicted…
We present a Bayesian algorithm to combine optical imaging of unresolved objects from distinct epochs and observation platforms for orbit determination and tracking. By propagating the non-Gaussian uncertainties we are able to optimally…