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We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the…
We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the…
This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs.…
We consider a discrete elliptic equation on the $d$-dimensional lattice $\mathbb{Z}^d$ with random coefficients $A$ of the simplest type: they are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice…
Gradient clipping is an important technique for deep neural networks with exploding gradients, such as recurrent neural networks. Recent studies have shown that the loss functions of these networks do not satisfy the conventional smoothness…
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…
We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497--A519 (2012)] to elliptic problems with mixed boundary conditions and elliptic…
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume…
This paper studies line planning for urban bus networks that face multiple resource limits such as budget, labor, and emission caps while using heterogeneous fleets. The objective is to maximize total reward from serving passengers by…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
We consider the optimal decision-making problem in a primary sample of interest with multiple auxiliary sources available. The outcome of interest is limited in the sense that it is only observed in the primary sample. In reality, such…
Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the…
We derive lower bounds on the black-box oracle complexity of large-scale smooth convex minimization problems, with emphasis on minimizing smooth (with Holder continuous, with a given exponent and constant, gradient) convex functions over…
In this paper, we consider the finite element approximation for a parabolic problem on a smooth domain $\Omega \subset \mathbb{R}^N$ with the inhomogeneous Neumann boundary condition. We emphasize that the domain can be non-convex in…