Results 1  10
of
1,446,164
Lower bounds for the number of small convex kholes
, 2012
"... Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdőstype question on the least number hk(n) of convex kholes in S, and give improved lower bounds on hk(n), for 3 ≤ k ≤ 5. Specifically, we show that h3(n) ≥ n2 − 32n7 + 227, ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdőstype question on the least number hk(n) of convex kholes in S, and give improved lower bounds on hk(n), for 3 ≤ k ≤ 5. Specifically, we show that h3(n) ≥ n2 − 32n7 + 227
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
Abstract

Cited by 5350 (67 self)
 Add to MetaCart
was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
On kGons and kHoles in Point Sets
"... We consider a variation of the classical ErdősSzekeres problems on the existence and number of convex kgons and kholes (empty kgons) in a set of n points in the plane. Allowing the kgons to be nonconvex, we show bounds and structural results on maximizing and minimizing their numbers. Most not ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
noteworthy, for any k and sufficiently large n, we give a quadratic lower bound for the number of kholes, and show that this number is maximized by sets in convex position. We also provide an improved lower bound for the number of convex 6holes. 1
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
Abstract

Cited by 496 (2 self)
 Add to MetaCart
. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
Abstract

Cited by 557 (9 self)
 Add to MetaCart
An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Blocking the kholes of point sets on the plane
 XIV SPANISH MEETING ON COMPUTATIONAL GEOMETRY, 27–30 JUNE 2011
, 2011
"... Let P be a set of n points in the plane in general position. A subset hk of k points of P is called a khole if there is no element of P contained in the interior of the convex hull of hk. A set B of points blocks the kholes of P if any khole of P contains an element of B in its interior. In this ..."
Abstract
 Add to MetaCart
. In this paper we establish upper and lower bounds on the sizes of khole blocking sets.
GPSless Low Cost Outdoor Localization For Very Small Devices
, 2000
"... Instrumenting the physical world through large networks of wireless sensor nodes, particularly for applications like environmental monitoring of water and soil, requires that these nodes be very small, light, untethered and unobtrusive. The problem of localization, i.e., determining where a given no ..."
Abstract

Cited by 994 (29 self)
 Add to MetaCart
Instrumenting the physical world through large networks of wireless sensor nodes, particularly for applications like environmental monitoring of water and soil, requires that these nodes be very small, light, untethered and unobtrusive. The problem of localization, i.e., determining where a given
Results 1  10
of
1,446,164