Results 1  10
of
494,853
A Nonlinear Programming Algorithm for Solving Semidefinite Programs via Lowrank Factorization
 Mathematical Programming (series B
, 2001
"... In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according ..."
Abstract

Cited by 153 (10 self)
 Add to MetaCart
computational results on some largescale test problems are also presented. Keywords: semidefinite programming, lowrank factorization, nonlinear programming, augmented Lagrangian, limited memory BFGS. 1 Introduction In the past few years, the topic of semidefinite programming, or SDP, has received
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
Abstract

Cited by 780 (22 self)
 Add to MetaCart
problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
Abstract

Cited by 1231 (13 self)
 Add to MetaCart
the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Local minima and convergence in lowrank semidefinite programming
 Mathematical Programming
, 2003
"... The lowrank semidefinite programming problem (LRSDPr) is a restriction of the semidefinite programming problem (SDP) in which a bound r is imposed on the rank of X, and it is well known that LRSDPr is equivalent to SDP if r is not too small. In this paper, we classify the local minima of LRSDPr and ..."
Abstract

Cited by 44 (2 self)
 Add to MetaCart
The lowrank semidefinite programming problem (LRSDPr) is a restriction of the semidefinite programming problem (SDP) in which a bound r is imposed on the rank of X, and it is well known that LRSDPr is equivalent to SDP if r is not too small. In this paper, we classify the local minima of LRSDPr
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
Abstract

Cited by 557 (12 self)
 Add to MetaCart
We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Fast lowrank semidefinite programming for embedding and clustering
 in Eleventh International Conference on Artifical Intelligence and Statistics, AISTATS 2007
, 2007
"... Many nonconvex problems in machine learning such as embedding and clustering have been solved using convex semidefinite relaxations. These semidefinite programs (SDPs) are expensive to solve and are hence limited to run on very small data sets. In this paper we show how we can improve the quality a ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
and speed of solving a number of these problems by casting them as lowrank SDPs and then directly solving them using a nonconvex optimization algorithm. In particular, we show that problems such as the kmeans clustering and maximum variance unfolding (MVU) may be expressed exactly as lowrank SDPs
Lowrank optimization for semidefinite convex problems ∗
, 807
"... Compiled on July 28, 2008, 12:05 We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable X. This algorithm rests on the factorization X = Y Y T, where the number of columns of Y fixes the rank of X. It is thus very effective ..."
Abstract

Cited by 12 (8 self)
 Add to MetaCart
Compiled on July 28, 2008, 12:05 We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable X. This algorithm rests on the factorization X = Y Y T, where the number of columns of Y fixes the rank of X. It is thus very
LOWRANK OPTIMIZATION ON THE CONE OF POSITIVE SEMIDEFINITE MATRICES ∗
"... Abstract. We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = YYT, where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X ..."
Abstract

Cited by 28 (6 self)
 Add to MetaCart
Abstract. We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = YYT, where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix
Results 1  10
of
494,853