Related papers: Partial $\ell_1$ optimization in random linear sys…
The use of partition function zeros in the study of phase transition is growing in the last decade mainly due to improved numerical methods as well as novel formulations and analysis. In this paper the impact of different parameters choice…
Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing…
In this paper, we propose and study the use of alternating direction algorithms for several $\ell_1$-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the…
Reducing the fuel consumption within a power network is crucial to enhance the overall system efficiency and minimize operating costs. Fuel consumption minimization can be achieved through different optimization techniques where the output…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…
We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
In this paper, we are interested in optimal decisions in a partially observable Markov universe. Our viewpoint departs from the dynamic programming viewpoint: we are directly approximating an optimal strategic tree depending on the…
Companion paper [118] developed a powerful \emph{Random duality theory} (RDT) based analytical program to statistically characterize performance of \emph{descending} phase retrieval algorithms (dPR) (these include all variants of gradient…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
Maximizing the Kullback-Leibler divergence (KLD) is a fundamental problem in waveform design for active sensing and hypothesis testing, as it directly relates to the error exponent of detection probability. However, the associated…
This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity)…
In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only…
We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the $\ell_2$ setting achieves optimal…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a…