Related papers: On the existence of optimizers for time-frequency …
We consider a class of convex optimization problems over the simplex of probability measures. Our framework comprises optimal experimental design (OED) problems, in which the measure over the design space indicates which experiments are…
We consider the problem of approximating the unknown density $u\in L^2(\Omega,\lambda)$ of a measure $\mu$ on $\Omega\subset\R^n$, absolutely continuous with respect to some given reference measure $\lambda$, from the only knowledge of…
In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. The goal is to find a subset of elements along with an associated set of bins, such…
We study the optimal sets $\Omega^\ast\subset\mathbb{R}^d$ for spectral functionals $F\big(\lambda_1(\Omega),\dots,\lambda_p(\Omega)\big)$, which are bi-Lipschitz with respect to each of the eigenvalues…
When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here we study the problem of how to optimally…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
In this paper we consider the scale invariant shape functional $${\mathcal{F}}_{p,q}(\Omega)=\frac{\lambda_p^{1/p}(\Omega)}{\lambda_q^{1/q}(\Omega)},$$ where $1\le q<p\le+\infty$ and $\lambda_p(\Omega)$ (respectively $\lambda_q(\Omega)$) is…
We show an improved lower bound for the Fp estimation problem in a data stream setting for p>2. A data stream is a sequence of items from the domain [n] with possible repetitions. The frequency vector x is an n-dimensional non-negative…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
This paper establishes the strict optimality in precision for frequency and distribution estimation under local differential privacy (LDP). We prove that a linear estimator with a symmetric and extremal configuration, and a constant support…
We consider minimization problems for curves of measure, with kinetic and potential energy and a congestion penalization, as in the functionals that appear in Mean Field Games with a variational structure. We prove L infinity regularity…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
Let $f:\Omega\to\IR^2$ be a mapping of finite distortion, where $\Omega\subset\IR^2 .$ Assume that the distortion function $K(x,f)$ satisfies $e^{K(\cdot, f)}\in L^p_{loc}(\Omega)$ for some $p>0.$ We establish optimal regularity and area…
We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for…
Among subsets of Euclidean space with prescribed measure, for which sets is the $L^q$ norm of the Fourier transform of the indicator function maximized? Various partial results concerning this question are established, including the…
In this paper, we investigate the minimization problem : $$ \inf_{ \displaystyle{\begin{array}{lll} u \in H_0^1(\Omega), v \in H_0^1(\Omega),\\ \quad \| u \|_{L^{q}} =1, \quad \| v \|_{L^{q}} = 1 \end{array}}} \left[ \frac{1}{2}…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…