Results 1  10
of
75
Which nonnegative matrices are slack matrices?
, 2013
"... In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. The underlying decision problem is equivalent to the polyhedral verification problem whose complexity is unknown. ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. The underlying decision problem is equivalent to the polyhedral verification problem whose complexity is unknown.
LMI tests for positive definite polynomials: Slack variable approach
 IEEE Trans. on Automatic Control
"... The considered problem is assessing nonnegativity of a function’s values when indeterminates are in domains constrained by scalar polynomial inequalities. The tested functions are multiindeterminates polynomial matrices which are required to be positive semidefinite. For such problems new tests b ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
based on linear matrix inequalities are provided in a Slack Variables type approach. The results are compared to those obtained via the SumOfSquares approach, are proved to be equivalent in case of unbounded domains and less conservative if polytopictype bounds are known.
R.: Approximate cone factorizations and lifts of polytopes
, 2013
"... Abstract. In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonn ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact
New robust stability and stabilization conditions for linear repetitive processes New Robust Stability and Stabilization Conditions for Linear Repetitive Processes
"... AbstractThis paper focuses on the problem of robust stabilization for differential or discrete linear repetitive processes. The provided conditions allow us to involve parameter dependent Lyapunov functions. An additional flexibility in finding a solution is obtained by introducing slack matrix va ..."
Abstract
 Add to MetaCart
AbstractThis paper focuses on the problem of robust stabilization for differential or discrete linear repetitive processes. The provided conditions allow us to involve parameter dependent Lyapunov functions. An additional flexibility in finding a solution is obtained by introducing slack matrix
A Note on Efficient Computation of the Gradient in Semidefinite Programming
, 1999
"... In the GoemansWilliamson semidefinite relaxation of MAXCUT, the gradient of the dual barrier objective function has a term of the form diag(Z 1 ), where Z is the slack matrix. The purpose of this note is to show that this term can be computed in time and space proportional to the time and space f ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
In the GoemansWilliamson semidefinite relaxation of MAXCUT, the gradient of the dual barrier objective function has a term of the form diag(Z 1 ), where Z is the slack matrix. The purpose of this note is to show that this term can be computed in time and space proportional to the time and space
1Fixedorder Controller Design of Linear Systems*
, 2014
"... The problem of fixedorder dynamic output feedback control of systems subject to polytopic uncertainties is a challenging issue in the community of robust control theory. Various LMIbased methods have been developed since the last decade. In this report, we show that most of slackmatrix based meth ..."
Abstract
 Add to MetaCart
The problem of fixedorder dynamic output feedback control of systems subject to polytopic uncertainties is a challenging issue in the community of robust control theory. Various LMIbased methods have been developed since the last decade. In this report, we show that most of slackmatrix based
Query complexity in expectation
, 2014
"... We study the query complexity of computing a function f: {0, 1}n → R+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as possible. We exactly characterize both the randomized and the qu ..."
Abstract
 Add to MetaCart
with range {0, 1}. These query complexities relate to (and are motivated by) the extension complexity of polytopes. The linear extension complexity of a polytope is characterized by the randomized communication complexity of computing its slack matrix in expectation, and the semidefinite (psd) extension
Table 1. THE PRODUCTPROCESS MATRIX
"... This explores Schmenner's predictions of the productprocess matrix using book printing firms in S.A. It measures focus in each book printing firm, and then examines relationships between measures. This study finds that these measures are not well behaved in the way Schmenner predicts and more ..."
Abstract
 Add to MetaCart
changes, product mix changes. On the product mix axis the product variety reduces as volumes increase. Both Schmenner and Slack (1991, p. 129) show the shaded areas (off diagonal) as being high cost areas in the productprocess matrix. Others point to parts of this association. For example Hill (1985, p
An Improved DelayDependent Stability Criterion for a Class of Lur'e Systems of Neutral Type
"... In this paper, we consider the problem of delaydependent stability of a class of Lur'e systems of neutral type with timevarying delays and sectorbounded nonlinearity using LyapunovKrasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less cons ..."
Abstract
 Add to MetaCart
minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical
Lifts of convex sets and cone factorizations
 Mathematics of OR
"... Abstract. In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone. Such a representation or “lift ” of the convex set is especially useful if the cone admits an efficient algorithm for linear op ..."
Abstract

Cited by 21 (8 self)
 Add to MetaCart
between polyhedral lifts of a polytope and nonnegative factorizations of its slack matrix. Symmetric lifts of convex sets can also be characterized similarly. When the cones live in a family, our results lead to the definition of the rank of a convex set with respect to this family. We present results
Results 1  10
of
75