Results 1  10
of
917,919
An Accelerated Interior Point Method Whose Running Time Depends Only on A
 IN PROCEEDINGS OF 26TH ANNUAL ACM SYMPOSIUM ON THE THEORY OF COMPUTING
, 1993
"... We propose a "layeredstep" interior point (LIP) algorithm for linear programming. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares" (LLS) step. The algorithm returns the exact global minimum after a finit ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
finite number of stepsin particular, after O(n 3:5 c(A)) iterations, where c(A) is a function of the coefficient matrix. The LLS steps can be thought of as accelerating a pathfollowing interior point method whenever neardegeneracies occur. One consequence of the new method is a new
Interiorpoint Methods
, 2000
"... The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadrati ..."
Abstract

Cited by 598 (15 self)
 Add to MetaCart
The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex
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 543 (12 self)
 Add to MetaCart
to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
Abstract

Cited by 2684 (61 self)
 Add to MetaCart
successfully only because of recent advances in linear programming by interiorpoint methods. We obtain reasonable success with a primaldual logarithmic barrier method and conjugategradient solver.
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
Abstract

Cited by 530 (21 self)
 Add to MetaCart
of recovering a large matrix from a small subset of its entries (the famous Netflix problem). Offtheshelf algorithms such as interior point methods are not directly amenable to large problems of this kind with over a million unknown entries. This paper develops a simple firstorder and easy
Multiple kernel learning, conic duality, and the SMO algorithm
 In Proceedings of the 21st International Conference on Machine Learning (ICML
, 2004
"... While classical kernelbased classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimiz ..."
Abstract

Cited by 442 (31 self)
 Add to MetaCart
the technique of MoreauYosida regularization to yield a formulation to which SMO techniques can be applied. We present experimental results that show that our SMObased algorithm is significantly more efficient than the generalpurpose interior point methods available in current optimization toolboxes. 1.
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 250 (19 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
Fast linear iterations for distributed averaging.
 Systems & Control Letters,
, 2004
"... Abstract We consider the problem of finding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of finding the fastest converging ..."
Abstract

Cited by 421 (12 self)
 Add to MetaCart
be exploited to speed up interiorpoint methods for solving the fastest distributed linear iteration problem, for networks with up to a thousand or so edges. We also describe a simple subgradient method that handles far larger problems, with up to one hundred thousand edges. We give several extensions
Robust convex optimization
 Mathematics of Operations Research
, 1998
"... We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we la ..."
Abstract

Cited by 406 (21 self)
 Add to MetaCart
) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficient algorithms such as polynomial time interior point methods.
An interiorpoint method for largescale l1regularized logistic regression
 Journal of Machine Learning Research
, 2007
"... Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand ..."
Abstract

Cited by 278 (8 self)
 Add to MetaCart
Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand
Results 1  10
of
917,919