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A Homogeneous Interiorpoint Algorithm for . . .
"... A homogeneous infeasiblestart interiorpoint algorithm for solving nonsymmetric convex conic optimization problems is presented. Starting each iteration from the vicinity of the central path, the method steps in the approximate tangent direction and then applies a correction phase to locate the ne ..."
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A homogeneous infeasiblestart interiorpoint algorithm for solving nonsymmetric convex conic optimization problems is presented. Starting each iteration from the vicinity of the central path, the method steps in the approximate tangent direction and then applies a correction phase to locate
The homogeneous interiorpoint algorithm: Nonsymmetric cones, . . .
, 2013
"... The overall topic of this thesis is convex conic optimization, a subfield of mathematical optimization that attacks optimization problem with a certain geometric structure. These problems allow for modelling of an extremely wide range of realworld problems, but the availability of solution algori ..."
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Cited by 4 (0 self)
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algorithms for these problems is still limited. The goal of this thesis is to investigate and shed light on two computational aspects of homogeneous interiorpoint algorithms for convex conic optimization: The first part studies the possibility of devising a homogeneous interiorpoint method aimed
Homogeneous InteriorPoint Algorithms for Semidefinite Programming
 Department of Mathematics, The University of Iowa
, 1995
"... A simple homogeneous primaldual feasibility model is proposed for semidefinite programming (SDP) problems. Two infeasibleinteriorpoint algorithms are applied to the homogeneous formulation. The algorithms do not need big M initialization. If the original SDP problem has a solution, then both algo ..."
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Cited by 37 (8 self)
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, homogeneous interiorpoint algorithm, polynomial complexity. Abbreviated Title: Homogeneous al...
SDPHA  a MATLAB implementation of homogeneous interiorpoint algorithms for semidefinite programming
, 1997
"... Merhotra type primaldual predictorcorrector interiorpoint algorithms for semidefinite programming are implemented by using the homogeneous formulation proposed and analyzed by Potra and Sheng. Three different search directions  the AHO direction, the HKM direction, and the NT direction, are use ..."
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Cited by 16 (3 self)
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Merhotra type primaldual predictorcorrector interiorpoint algorithms for semidefinite programming are implemented by using the homogeneous formulation proposed and analyzed by Potra and Sheng. Three different search directions  the AHO direction, the HKM direction, and the NT direction
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 ..."
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Cited by 607 (15 self)
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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 ..."
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Cited by 548 (12 self)
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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 POLYNOMIALTIME ALGORITHM FOR LINEAR PROGRAMMING
 COMBINATORICA
, 1984
"... We present a new polynomialtime 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 ..."
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Cited by 857 (3 self)
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the ellipsoid algorithm by a factor of O(n~'~). We prove that given a polytope P and a strictly interior point a E P, there is a projective transformation of the space that maps P, a to P', a ' having the following property. The ratio of the radius of the smallest sphere with center a
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 ..."
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Cited by 553 (21 self)
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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
Results 1  10
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465,847