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Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
We propose a class of very simple modifications of gradient descent and stochastic gradient descent. We show that when applied to a large variety of machine learning problems, ranging from logistic regression to deep neural nets, the…
This work introduces a new higher-order super-compact (HOSC) implicit finite difference scheme for analyzing three-dimensional (3D) natural convection and entropy generation in non-Newtonian fluids. The proposed scheme achieves fourth-order…
Consensus-based optimization (CBO) is a powerful and versatile zero-order multi-particle method designed to provably solve high-dimensional global optimization problems, including those that are genuinely nonconvex or nonsmooth. The method…
Dynamic pricing is the practice of adjusting the selling price of a product to maximize a firm's revenue by responding to market demand. The literature typically distinguishes between two settings: infinite inventory, where the firm has…
ExponenTial Smoothing (ETS) is a widely adopted forecasting technique in both research and practical applications. One critical development in ETS was the establishment of a robust statistical foundation based on state space models with a…
In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
We derive a variant of the nonsmooth maximum principle for problems with pure state constraints. The interest of our result resides on the nonsmoothness itself since, when applied to smooth problems, it coincides with known results.…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative…
A hyperbolic integro-differential equation is considered, as a model problem, where the convolution kernel is assumed to be either smooth or no worse than weakly singular. Well-posedness of the problem is studied in the context of semigroup…
This study presents a comprehensive approach to optimizing inventory management under stochastic demand by leveraging Monte Carlo Simulation (MCS) with grid search and Bayesian optimization. By using a business case of historical demand…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
In this work, we design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection…
Particles on Demand formulation of kinetic theory [B. Dorschner, F. B\"{o}sch and I. V. Karlin, {\it Phys. Rev. Lett.} {\bf 121}, 130602 (2018)] is used to simulate a variety of compressible flows with strong discontinuities in density,…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered…
In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…