相关论文: Turnpike with Uncertain Measurements: Triangle-Equ…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from…
Information-theoretic uncertainty relations formulate the joint immeasurability of two non-commuting observables in terms of information entropies. The trade-off of the accuracy in the outcome of two successive measurements manifests in…
Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity…
In this manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show that the turnpike effect persists in the presence of noise…
In this paper, we propose a fast and convergent algorithm to solve unassigned distance geometry problems (uDGP). Technically, we construct a novel quadratic measurement model by leveraging $\ell_0$-norm instead of $\ell_1$-norm in the…
This paper studies discounted Markov Decision Processes (MDPs) with finite sets of states and actions. Value iteration is one of the major methods for finding optimal policies. For each discount factor, starting from a finite number of…
Environmental monitoring robots often need to estimate data fields (e.g., salinity, temperature, bathymetry) under tight resource constraints. Classical boustrophedon lawnmower surveys provide geometric coverage guarantees but can waste…
In this paper we study an application of an information distance between two measurements to the problem of non-contextuality and local realism. We postulate the triangle principle which states that any information distance is well defined…
We introduce and study the turnpike property for time-varying shapes, within the viewpoint of optimal control. We focus here on second-order linear parabolic equations where the shape acts as a source term and we seek the optimal…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
In this work, we consider the problem of multi-pitch estimation, i.e., identifying super-imposed truncated harmonic series from noisy measurements. We phrase this as recovering a harmonically-structured measure on the unit circle, where the…
Many inverse problems in signal processing deal with the robust estimation of unknown data from underdetermined linear observations. Low dimensional models, when combined with appropriate regularizers, have been shown to be efficient at…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
We establish the turnpike property for linear quadratic control problems for which the control operator is admissible and may be unbounded, under quite general and natural assumptions. The turnpike property has been well studied for bounded…
We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the…
This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…
In this paper we investigate the turnpike property for constrained LQ optimal control problem in connection with dissipativity of the control system. We determine sufficient conditions to ensure the turnpike property in the case of a…
This paper presents an average case denoising performance analysis for the Subspace Pursuit (SP), the CoSaMP and the IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that (i) it is corrupted by an…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
We consider a constrained eigenvalue optimization problem that arises in an important nonlinear dynamical model for mRNA translation in the cell. We prove that the ordered list of optimal parameters admits a turnpike property, namely, it…