LOQO: An interior point code for quadratic programming

Robert J. Vanderbei

Research output: Contribution to journalArticlepeer-review

225 Scopus citations


This paper describes a software package, called LOQO, which implements a primal-dual interior-point 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 was 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.

Original languageEnglish (US)
Pages (from-to)451-484
Number of pages34
JournalOptimization Methods and Software
Issue number1
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Optimization
  • Applied Mathematics


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