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Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
In this paper, we study distributed optimization with smooth non-convex local objectives. We propose a novel variant of the well-known EXact firsT-ordeR Algorithm (EXTRA), called Two-timescale EXTRA, by introducing two distinct step-sizes.…
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they…
A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…
We study the problem of learning shared structure \emph{across} a sequence of dynamic pricing experiments for related products. We consider a practical formulation where the unknown demand parameters for each product come from an unknown…
Competition is a main tenet of economics, and the reason is that a perfectly competitive equilibrium is Pareto-efficient in the absence of externalities and public goods. Whether a product is selected in a market crucially relates to its…
We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…
Many entropy-conservative and entropy-stable (summarized as entropy-preserving) methods for hyperbolic conservation laws rely on Tadmor's theory for two-point entropy-preserving numerical fluxes and its higher-order extension via flux…
We develop a principled approach to obtain exact computer-aided worst-case guarantees on the performance of second-order optimization methods on classes of univariate functions. We first present a generic technique to derive interpolation…
We consider the resource allocation problem and its numerical solution. The following constructions are demonstrated: 1) Walrasian price-adjustment mechanism for determining the equilibrium; 2) Decentralized role of the prices; 3) Slater's…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. Error estimates are…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced…
Two-time-scale stochastic approximation is a popular iterative method for finding the solution of a system of two equations. Such methods have found broad applications in many areas, especially in machine learning and reinforcement…
We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…
Classical algorithms for market equilibrium computation such as proportional response dynamics face scalability issues with Internet-based applications such as auctions, recommender systems, and fair division, despite having an almost…
The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in…
Shallow water moment equations are reduced-order models for free-surface flows that allow to represent vertical variations of the velocity profile at the expense of additional evolution equations for a number of additional variables, so…