Related papers: High order concentrated non-negative matrix-expone…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory…
In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric…
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…
This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
This work presents an approach to the inverse design of scattering systems by modifying the transmission matrix using reinforcement learning. We utilize Proximal Policy Optimization to navigate the highly non-convex landscape of the object…
Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the "curse of dimensionality", an exponential cost…
The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable function vectors and related multi-wavelets is well studied. In…
Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty…
Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…