Results 1 - 10 of 6,066

Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization

by Farid Alizadeh - 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 547 (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

A NEW POLYNOMIAL-TIME ALGORITHM FOR LINEAR PROGRAMMING

by N. Karmarkar - COMBINATORICA , 1984
"... We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ell ..."
Abstract - Cited by 860 (3 self) - Add to MetaCart
', containing P ' to the radius of the largest sphere with center a ' contained in P ' is O(n). The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal

Efficiently computing static single assignment form and the control dependence graph

by Ron Cytron, Jeanne Ferrante, Barry K. Rosen, Mark N. Wegman, F. Kenneth Zadeck - ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS , 1991
"... In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single ass ..."
Abstract - Cited by 1003 (8 self) - Add to MetaCart
In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single

Training Support Vector Machines: an Application to Face Detection

by Edgar Osuna, Robert Freund, Federico Girosi , 1997
"... We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision sur ..."
Abstract - Cited by 727 (1 self) - Add to MetaCart
surfaces are found by solving a linearly constrained quadratic programming problem. This optimization problem is challenging because the quadratic form is completely dense and the memory requirements grow with the square of the number of data points. We present a decomposition algorithm that guarantees

ATOMIC DECOMPOSITION BY BASIS PURSUIT

by Scott Shaobing Chen , David L. Donoho , Michael A. Saunders , 1995
"... The Time-Frequency and Time-Scale 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 2728 (61 self) - Add to MetaCart
variation de-noising, and multi-scale edge denoising. Basis Pursuit in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked

FFTW: An Adaptive Software Architecture For The FFT

by Matteo Frigo, Steven G. Johnson , 1998
"... FFT literature has been mostly concerned with minimizing the number of floating-point operations performed by an algorithm. Unfortunately, on present-day microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have ..."
Abstract - Cited by 602 (4 self) - Add to MetaCart
FFT literature has been mostly concerned with minimizing the number of floating-point operations performed by an algorithm. Unfortunately, on present-day microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have

Estimating the Support of a High-Dimensional Distribution

by Bernhard Schölkopf, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson , 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
Abstract - Cited by 783 (29 self) - Add to MetaCart
of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a preliminary theoretical analysis of the statistical performance of our

Robust convex optimization

by A. Ben-tal, A. Nemirovski - 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 416 (21 self) - Add to MetaCart
lay the foundation of robust convex optimization. In the main part of the paper we show that if U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others

Multiple kernel learning, conic duality, and the SMO algorithm

by Francis R. Bach, Gert R. G. Lanckriet - In Proceedings of the 21st International Conference on Machine Learning (ICML , 2004
"... While classical kernel-based 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 445 (31 self) - Add to MetaCart
that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadratically-constrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points

A first-order primal-dual algorithm for convex problems with applications to imaging

by Antonin Chambolle, Thomas Pock , 2010
"... In this paper we study a first-order primal-dual algorithm for convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) in finite dimensions, which is optimal for the complete class of non-smooth problems we are considering in this paper ..."
Abstract - Cited by 436 (20 self) - Add to MetaCart
In this paper we study a first-order primal-dual algorithm for convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) in finite dimensions, which is optimal for the complete class of non-smooth problems we are considering
Results 1 - 10 of 6,066