Related papers: Full Recovery from Point Values: an Optimal Algori…
Operation management problems (such as Production Planning and Scheduling) are represented and formulated as optimization models. The resolution of such optimization models leads to solutions which have to be operated in an organization.…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to…
Suppose a graph $G$ is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to…
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$…
We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be…
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
The goal of model-based diagnosis is to isolate causes of anomalous system behavior and recommend inexpensive repair actions in response. In general, precomputing optimal repair policies is intractable. To date, investigators addressing…
We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…
We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
In this paper, we demonstrate the application of generalised rational uniform (Chebyshev) approximation in neural networks. In particular, our activation functions are one degree rational functions and the loss function is based on the…
This paper studies function approximation in Gaussian Sobolev spaces over the real line and measures the error in a Gaussian-weighted $L^p$-norm. We construct two linear approximation algorithms using $n$ function evaluations that achieve…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
We consider the problem of recovering characteristic functions $u:=\chi_\Omega$ from cell-average data on a coarse grid, and where $\Omega$ is a compact set of $\mathbb{R}^d$. This task arises in very different contexts such as image…