A parallel formulation of interior point algorithms

In recent years, interior point algorithms have been used successfully for solving mediumto large-size linear programming LP problems. In this paper we describe a highly parallel formulation of the interior point algorithm. A key component of the interior point algorithm is the solutionofasparse system oflinear equations using Cholesky factorization. The performance of parallel Cholesky factorization is determined by a the communication overhead incurred by the algorithm, and b the load imbalance among the processors. In our parallel interior point algorithm, we use our recently developed parallel multifrontal algorithm that has the smallest communication overhead over all parallel algorithms for Cholesky factorization developed to date. The computation imbalance depends on the shape of the elimination tree associated with the sparse system reordered for factorization. To balance the computation, we implemented and evaluated four di erent ordering algorithms. Among these algorithms, K...

• Type: Conference
• Year: 1994
• Where: SC
• Authors: George Karypis, Anshul Gupta, Vipin Kumar
• Keywords: Applied Computing, Cholesky Factorization, Interior Point Algorithm, Parallel Cholesky Factorization, SC 1994