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44
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 207 (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 applications include maxmin eigenvalue problems and relaxations for the stable set problem.
LOQO: An interior point code for quadratic programming
, 1994
"... ABSTRACT. This paper describes a software package, called LOQO, which implements a primaldual interiorpoint method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex ..."
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Cited by 154 (9 self)
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ABSTRACT. This paper describes a software package, called LOQO, which implements a primaldual interiorpoint method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex and general nonlinear programming, since a detailed paper describing these extensions were published recently elsewhere. In particular, we emphasize the importance of establishing and maintaining symmetric quasidefiniteness of the reduced KKT system. We show that the industry standard MPS format can be nicely formulated in such a way to provide quasidefiniteness. Computational results are included for a variety of linear and quadratic programming problems. 1.
Sequential Quadratic Programming
, 1995
"... this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can ..."
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Cited by 117 (3 self)
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this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can
Implementation of interior point methods for large scale linear programming
 Interior point methods in mathematical programming
, 1996
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Computational Study of a Family of MixedInteger Quadratic Programming Problems
 Mathematical programming
, 1995
"... . We present computational experience with a branchandcut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest reallife problems in a few minutes of run ..."
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Cited by 48 (6 self)
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. We present computational experience with a branchandcut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest reallife problems in a few minutes of runtime. 1 Introduction. We are interested in optimization problems QMIP of the form: min x T Qx + c T x s.t. Ax b (1) jsupp(x)j K (2) 0 x j u j ; all j (3) where x is an nvector, Q is a symmetric positivesemidefinite matrix, supp(x) = fj : x j ? 0g and K is a positive integer. Problems of this type are of interest in portfolio optimization. Briefly, variables in the problem correspond to commodities to be bought, the objective is a measure of "risk", the constraints (1) prescribe levels of "performance", and constraint (2) specifies that not too many 1 different types of commodities can be chosen. All data is derived from statistical information. A good deal of previous work ha...
A QMRbased interiorpoint algorithm for solving linear programs”, AT&T Bell Laboratories and Institute für Angewandte Mathematik und Statistik
, 1995
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Presolve analysis of linear programs prior to applying an interior point method
 INFORMS Journal on Computing
, 1997
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Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization
 Optimization Methods and Software
, 1999
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A Bundle Type DualAscent Approach to Linear Multicommodity MinCost Flow Problems
, 1999
"... ... MinCost Flow problem, where the mutual capacity constraints are dualized and the resulting Lagrangean Dual is solved with a dualascent algorithm belonging to the class of Bundle methods. Although decomposition approaches to blockstructured Linear Programs have been reported not to be competit ..."
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Cited by 26 (14 self)
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... MinCost Flow problem, where the mutual capacity constraints are dualized and the resulting Lagrangean Dual is solved with a dualascent algorithm belonging to the class of Bundle methods. Although decomposition approaches to blockstructured Linear Programs have been reported not to be competitive with generalpurpose software, our extensive computational comparison shows that, when carefully implemented, a decomposition algorithm can outperform several other approaches, especially on problems where the number of commodities is “large” with respect to the size of the graph. Our specialized Bundle algorithm is characterized by a new heuristic for the trust region parameter handling, and embeds a specialized Quadratic Program solver that allows the efficient implementation of strategies for reducing the number of active Lagrangean variables. We also exploit the structural properties of the singlecommodity MinCost Flow subproblems to reduce the overall computational cost. The proposed approach can be easily extended to handle variants of the problem.