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NesterovTodd Directions are Newton Directions
, 1999
"... The theory of selfscaled conic programming provides a unified framework for the theories of linear programming, semidefinite programming and convex quadratic programming with convex quadratic constraints. The standard search directions for interiorpoint methods applied to selfscaled conic programm ..."
The GaussNewton Direction in Semidefinite Programming
, 1998
"... Primaldual interiorpoint methods have proven to be very successful for both linear programming (LP) and, more recently, for semidefinite programming (SDP) problems. Many of the techniques that have been so successful for LP have been extended to SDP. In fact, interior point methods are currently t ..."
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Cited by 5 (4 self)
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Primaldual interiorpoint methods have proven to be very successful for both linear programming (LP) and, more recently, for semidefinite programming (SDP) problems. Many of the techniques that have been so successful for LP have been extended to SDP. In fact, interior point methods are currently the only successful techniques for SDP.
A decomposition procedure based on approximate Newton directions.
 Mathematical Programming, Series A,
, 2002
"... Abstract. The efficient solution of largescale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions fr ..."
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Cited by 24 (2 self)
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Abstract. The efficient solution of largescale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions
A DECOMPOSITION PROCEDURE BASED ON APPROXIMATE NEWTON DIRECTIONS
"... The efficient solution of largescale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from decompos ..."
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The efficient solution of largescale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from
Detection and Tracking of Point Features
 International Journal of Computer Vision
, 1991
"... The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small interframe displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade i ..."
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Cited by 629 (2 self)
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leads to a NewtonRaphson style minimization. In this report, after rederiving the method in a physically intuitive way, we answer the crucial question of how to choose the feature windows that are best suited for tracking. Our selection criterion is based directly on the definition of the tracking
Cutting Planes and a Biased Newton Direction for Minimizing Quasiconvex Functions
"... H. Scolnik 2 A biased Newton direction is introduced for minimizing quasiconvex functions with bounded level sets. It is a generalization of the usual Newton's direction for strictly convex quadratic functions. This new direction can be derived from the intersection of approximating hyperplanes ..."
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H. Scolnik 2 A biased Newton direction is introduced for minimizing quasiconvex functions with bounded level sets. It is a generalization of the usual Newton's direction for strictly convex quadratic functions. This new direction can be derived from the intersection of approximating
Convergence of an infeasible shortstep pathfollowing algorithm based on the GaussNewton direction
, 2000
"... This short note proves the polynomial time convergence of a short step, approximate path following, interiorpoint primaldual algorithm for semidenite programs based on the GaussNewton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the rst proof of conve ..."
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This short note proves the polynomial time convergence of a short step, approximate path following, interiorpoint primaldual algorithm for semidenite programs based on the GaussNewton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the rst proof
CONVERGENCE OF A SHORTSTEP PRIMALDUAL ALGORITHM BASED ON THE GAUSSNEWTON DIRECTION
, 2003
"... We prove the theoretical convergence of a shortstep, approximate pathfollowing, interiorpoint primaldual algorithm for semidefinite programs based on the GaussNewton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for th ..."
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We prove the theoretical convergence of a shortstep, approximate pathfollowing, interiorpoint primaldual algorithm for semidefinite programs based on the GaussNewton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence
Implementation of PrimalDual Methods for Semidefinite Programming Based on Monteiro and Tsuchiya Newton Directions and their Variants
 TECHNICAL REPORT, SCHOOL INDUSTRIAL AND SYSTEMS ENGINEERING, GEORGIA TECH., ATLANTA, GA 30332
, 1997
"... Monteiro and Tsuchiya [23] have proposed two primaldual Newton directions for semidefinite programming, referred to as the MT directions, and established polynomial convergence of path following methods based on them. This paper reports some computational results on the performance of interiorpoin ..."
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Cited by 22 (4 self)
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Monteiro and Tsuchiya [23] have proposed two primaldual Newton directions for semidefinite programming, referred to as the MT directions, and established polynomial convergence of path following methods based on them. This paper reports some computational results on the performance of interior
INTERIOR PATH FOLLOWING PRIMALDUAL ALGORITHMS. PART I: LINEAR PROGRAMMING
, 1989
"... We describe a primaldual interior point algorithm for linear programming problems which requires a total of O(~fnL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the KarushKuhnTucker system of equations w ..."
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Cited by 199 (11 self)
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We describe a primaldual interior point algorithm for linear programming problems which requires a total of O(~fnL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the KarushKuhnTucker system of equations
Results 1  10
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