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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 ..."
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Cited by 255 (18 self)
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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
Exploiting Sparsity in PrimalDual InteriorPoint Methods for Semidefinite Programming
 Mathematical Programming
, 1997
"... Abstract. The HelmbergRendlVanderbeiWolkowicz/KojimaShindohHara/Monteiro and the NesterovTodd search directions have been used in many primaldual interiorpoint methods for semidefinite programs. This paper proposes an efficient method for computing the two directions when a semidefinite prog ..."
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Cited by 80 (19 self)
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Abstract. The HelmbergRendlVanderbeiWolkowicz/KojimaShindohHara/Monteiro and the NesterovTodd search directions have been used in many primaldual interiorpoint methods for semidefinite programs. This paper proposes an efficient method for computing the two directions when a semidefinite
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 557 (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
Group symmetry in interiorpoint methods for semidefinite programming
 Optimization and Engineering
, 1970
"... Abstract A class of group symmetric SemiDefinite Program (SDP) is introduced by using the framework of group representation theory. It is proved that the central path and several search directions of primaldual interiorpoint methods are group symmetric. Preservation of group symmetry along the se ..."
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Cited by 15 (2 self)
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Abstract A class of group symmetric SemiDefinite Program (SDP) is introduced by using the framework of group representation theory. It is proved that the central path and several search directions of primaldual interiorpoint methods are group symmetric. Preservation of group symmetry along
Infeasible Interior Point Method for Semidefinite Programs
"... In Semidefinite programming one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive Semidefinite. Such a constraint is nonlinear and no smooth but convex,so semidefinite programs are convex optimization problems. Semidefinite programmin ..."
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general than linear programs, they are not much harder to solve. Most interior point methods for linear programming have been generalized to Semidefinite programs. However to find a strictly feasible initial point is difficult in practice. The notion of infeasible interior point algorithms introduced
Lagrangian Dual InteriorPoint Methods for Semidefinite Programs
 SIAM J. Optimization
, 2001
"... This paper proposes a new predictorcorrector interiorpoint method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished features of the method are full use of the BFGS quasiNewton method in the corrector procedu ..."
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Cited by 9 (1 self)
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This paper proposes a new predictorcorrector interiorpoint method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished features of the method are full use of the BFGS quasiNewton method in the corrector
A Note on the Calculation of StepLengths in InteriorPoint Methods for Semidefinite Programming
, 1999
"... . In each iteration of an interiorpoint method for semidefinite programming, the maximum steplength that can be taken by the iterate while maintaining the positive semidefiniteness constraint need to be estimated. In this note, we show how the maximum steplength can be estimated via the Lanczos i ..."
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Cited by 16 (4 self)
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. In each iteration of an interiorpoint method for semidefinite programming, the maximum steplength that can be taken by the iterate while maintaining the positive semidefiniteness constraint need to be estimated. In this note, we show how the maximum steplength can be estimated via the Lanczos
PrimalDual Interior Point Methods For Semidefinite Programming In Finite Precision
 SIAM J. Optimization
, 1997
"... . Recently, a number of primaldual interiorpoint methods for semidefinite programming have been developed. To reduce the number of floating point operations, each iteration of these methods typically performs block Gaussian elimination with block pivots that are close to singular near the optimal ..."
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Cited by 8 (0 self)
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. Recently, a number of primaldual interiorpoint methods for semidefinite programming have been developed. To reduce the number of floating point operations, each iteration of these methods typically performs block Gaussian elimination with block pivots that are close to singular near the optimal
A New PrimalDual InteriorPoint Method for Semidefinite Programming
, 1994
"... Semidefinite programming (SDP) is a convex optimization problem in the space of symmetric matrices. Primaldual interiorpoint methods for SDP are discussed. These generate primal and dual matrices X and Z which commute only in the limit. A new method is proposed which iterates in the space of commu ..."
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Cited by 11 (1 self)
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Semidefinite programming (SDP) is a convex optimization problem in the space of symmetric matrices. Primaldual interiorpoint methods for SDP are discussed. These generate primal and dual matrices X and Z which commute only in the limit. A new method is proposed which iterates in the space
Convergence analysis of an inexact infeasible interior point method for semidefinite programming
 Comput. Optim. Appl
"... Abstract. In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima, Megiddo and Mizuno (A primaldual infeasibleinteriorpoint algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use o ..."
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Cited by 5 (1 self)
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Abstract. In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima, Megiddo and Mizuno (A primaldual infeasibleinteriorpoint algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use
Results 1  10
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