Related papers: Learning polytopes with fixed facet directions

We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in $\R^d$. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension…

This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…

We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…

We study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal…

We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…

We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be…

Motivated by the analysis of the performance of the simplex method we study the behavior of families of pivot rules of linear programs. We introduce normalized-weight pivot rules which are fundamental for the following reasons: First, they…

Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator.…

This work deals with the problem of stabilizing a multi-agent rigid formation on a general class of planar curves. Namely, we seek to stabilize an equilateral polygonal formation on closed planar differentiable curves after a path sweep.…

A well-known result in the study of convex polyhedra, due to Minkowski, is that a convex polyhedron is uniquely determined (up to translation) by the directions and areas of its faces. The theorem guarantees existence of the polyhedron…

We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…

This paper studies a regularized support function estimator for bounds on components of the parameter vector in the case in which the identified set is a polygon. The proposed regularized estimator has three important properties: (i) it has…

A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab-initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines based methods…

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…

The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…

We present an improved algorithm for {\em quasi-properly} learning convex polyhedra in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polyhedron as an intersection of about $t \log t$…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

This work is concerned with fan- and cone-beam computed tomography with circular source trajectory, where the reconstruction inverse problem requires an accurate knowledge of source, detector and rotational axis relative positions and…