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CSDP, a C library for semidefinite programming.
, 1997
"... this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. ..."
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Cited by 206 (2 self)
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this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. Finally, we present results from the solution of a number of test problems. 2 The SDP Problem We consider semidefinite programming problems of the form max tr (CX)
A subspace semidefinite programming for spectral graph partit ioning
 Lecture Notes in Computer Science
, 2002
"... Abstract. A semidefinite program (SDP) is an optimization problem over n × n symmetric matrices where a linear function of the entries is to be minimized subject to linear equality constraints, and the condition that the unknown matrix is positive semidefinite. Standard techniques for solvingSDP’s r ..."
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Abstract. A semidefinite program (SDP) is an optimization problem over n × n symmetric matrices where a linear function of the entries is to be minimized subject to linear equality constraints, and the condition that the unknown matrix is positive semidefinite. Standard techniques for solvingSDP’s require O(n 3) operations per iteration. We introduce subspace algorithms that greatly reduce the cost os solving largescale SDP’s. We apply these algorithms to SDP approximations of graph partitioningproblems. We numerically compare our new algorithm with a standard semidefinite programming algorithm and show that our subspace algorithm performs better.
Distribution
"... Abstract. Graph partitioning with preferences is one of the data distribution models for parallel computer, where partitioning and mapping are generatedtogether. It improves the overall throughput of message traffic by having communication restrictedto processors which are near each other, whenever ..."
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Abstract. Graph partitioning with preferences is one of the data distribution models for parallel computer, where partitioning and mapping are generatedtogether. It improves the overall throughput of message traffic by having communication restrictedto processors which are near each other, whenever possible. This model is obtained by associating to each vertex a value which reflects its net preference for being in one partition or another of the recursive bisection process. We have formulated a semidefinite programming relaxation for graph partitioning with preferences andimplementedefficient subspace algorithm for this model. We numerically comparedour new algorithm with a standardsemidefinite programming algorithm andshow that our subspace algorithm performs better.