Related papers: Minoration via Mixed Volumes and Cover's Problem f…
We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
The important problem of weighted sum rate maximization (WSRM) in a multicellular environment is intrinsically sensitive to channel estimation errors. In this paper, we study ways to maximize the weighted sum rate in a linearly precoded…
This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…
We consider the problem of max-min fairness for uplink cell-free massive multiple-input multiple-output which is a potential technology for beyond 5G networks. More specifically, we aim to maximize the minimum spectral efficiency of all…
In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple…
We establish lower bounds on the volume and the surface area of a geometric body using the size of its slices along different directions. In the first part of the paper, we derive volume bounds for convex bodies using generalized…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
We investigate an alternative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy[1]. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and…
The primitive relay channel, introduced by Cover in 1987, is the simplest single-source single-destination network model that captures some of the most essential features and challenges of relaying in wireless networks. Recently, Wu and…
The famous Minkowski inequality provides a sharp lower bound for the mixed volume $V(K,M[n-1])$ of two convex bodies $K,M\subset\mathbb{R}^n$ in terms of powers of the volumes of the individual bodies $K$ and $M$. The special case where $K$…
We give a review of results on the minimum convex cover and maximum hidden set problems. In addition, we give some new results. First we show that it is NP-hard to determine whether a polygon has the same convex cover number as its hidden…
We propose a new topic modeling procedure that takes advantage of the fact that the Latent Dirichlet Allocation (LDA) log likelihood function is asymptotically equivalent to the logarithm of the volume of the topic simplex. This allows…
We take two new approaches to design efficient algorithms for transmitter optimization under rate constraints to guarantee the Quality of Service in general MIMO interference networks, named B-MAC Networks, which is a combination of…
In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of CNF formulas is always an upper bound on the width needed to refute them. Their proof is beautiful…
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We present an optimization model defined on the manifold of the set of stochastic matrices. Geometrically, the model is akin to identifying a maximum-volume $n$-dimensional simplex that has a given barycenter and is enclosed by the…
The capacity of a channel characterizes the maximum rate at which information can be transmitted through the channel asymptotically faithfully. For a channel with multiple senders and a single receiver, computing its sum capacity is…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…