Results 11  20
of
26,965
Semidefinite Programming and Combinatorial Optimization
 Appl. Numer. Math
, 1998
"... Semidefinite Programs have recently turned out to be a powerful tool for approximating integer problems. To survey the development in this area over the last few years, the following topics are addressed in some detail. First, we investigate ways to derive semidefinite programs from discrete opti ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
Semidefinite Programs have recently turned out to be a powerful tool for approximating integer problems. To survey the development in this area over the last few years, the following topics are addressed in some detail. First, we investigate ways to derive semidefinite programs from discrete
An InteriorPoint Method for Semidefinite Programming
, 2005
"... We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other appli ..."
Abstract

Cited by 255 (18 self)
 Add to MetaCart
We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other
Invariant semidefinite programs
 IN HANDBOOK ON SEMIDEFINITE, CONIC AND POLYNOMIAL OPTIMIZATION (M.F. ANJOS
, 2012
"... This chapter provides the reader with the necessary background for dealing with semidefinite programs which have symmetry. The basic theory is given and it is illustrated in applications from coding theory, combinatorics, geometry, and polynomial optimization. ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
This chapter provides the reader with the necessary background for dealing with semidefinite programs which have symmetry. The basic theory is given and it is illustrated in applications from coding theory, combinatorics, geometry, and polynomial optimization.
Semidefinite Programming Relaxation
"... Today, we talk the use of Semidefinite Programming in the design of approximation algorithms. This technique was invented by Goemans and Williamson in 1995. It is because of this technique both of them won the Fulkerson Prize in 2000. I’ll talk about this technique in the context of the ..."
Abstract
 Add to MetaCart
Today, we talk the use of Semidefinite Programming in the design of approximation algorithms. This technique was invented by Goemans and Williamson in 1995. It is because of this technique both of them won the Fulkerson Prize in 2000. I’ll talk about this technique in the context of the
The Volumetric Barrier for Semidefinite Programming
 Mathematics of Operations Research
, 1999
"... We consider the volumetric barrier for semidefinite programming, or "generalized" volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the volumetric barrier for a polyhedral set to the semidefinite case. Our analysis facilitates a simp ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We consider the volumetric barrier for semidefinite programming, or "generalized" volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the volumetric barrier for a polyhedral set to the semidefinite case. Our analysis facilitates a
On Weighted Centers For Semidefinite Programming
, 1996
"... In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the vspace framework, which is purely based on the symmetric primaldual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the weigh ..."
Abstract

Cited by 19 (6 self)
 Add to MetaCart
In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the vspace framework, which is purely based on the symmetric primaldual transformation and does not make use of barriers. Existence and scale invariance properties are proven
Regularization methods for semidefinite programming
 SIAM JOURNAL ON OPTIMIZATION
, 2009
"... We introduce a new class of algorithms for solving linear semidefinite programming (SDP) problems. Our approach is based on classical tools from convex optimization such as quadratic regularization and augmented Lagrangian techniques. We study the theoretical properties and we show that practical im ..."
Abstract

Cited by 45 (6 self)
 Add to MetaCart
We introduce a new class of algorithms for solving linear semidefinite programming (SDP) problems. Our approach is based on classical tools from convex optimization such as quadratic regularization and augmented Lagrangian techniques. We study the theoretical properties and we show that practical
Strong duality for semidefinite programming
 SIAM J. Optim
, 1997
"... Abstract. It is well known that the duality theory for linear programming (LP) is powerful and elegant and lies behind algorithms such as simplex and interiorpoint methods. However, the standard Lagrangian for nonlinear programs requires constraint qualifications to avoid duality gaps. Semidefinite ..."
Abstract

Cited by 64 (18 self)
 Add to MetaCart
. Semidefinite linear programming (SDP) is a generalization of LP where the nonnegativity constraints are replaced by a semidefiniteness constraint on the matrix variables. There are many applications, e.g., in systems and control theory and combinatorial optimization. However, the Lagrangian dual for SDP can
The Algebraic Degree of Semidefinite Programming
 LEIBNITZ UNIVERSITÄT HANNOVER, WELFENGARTEN 1, D30167 HANNOVER EMAIL ADDRESS: BOTHMER@MATH.UNIHANNOVER.DE URL: HTTP://WWW.IAG.UNIHANNOVER.DE/~BOTHMER/ MATEMATISK INSTITUTT, UNIVERSITETET I OSLO, PO BOX 1053, BLINDERN, NO0316
, 2008
"... Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear fu ..."
Abstract

Cited by 34 (10 self)
 Add to MetaCart
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear
Unsupervised Learning of Image Manifolds by Semidefinite Programming
, 2004
"... Can we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can be ..."
Abstract

Cited by 268 (10 self)
 Add to MetaCart
Can we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can
Results 11  20
of
26,965