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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 191 (10 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.
On Formulating Semidefinite Programming Problems As Smooth Convex Nonlinear Optimization Problems
, 2000
"... Consider the diagonal entries d j , j = 1, 2, . . . , n, of the matrix D in an LDL T factorization of an n ..."
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Cited by 12 (0 self)
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Consider the diagonal entries d j , j = 1, 2, . . . , n, of the matrix D in an LDL T factorization of an n
Solving Problems with Semidefinite and Related Constraints Using InteriorPoint Methods for Nonlinear Programming
, 2001
"... In this paper, we describe how to reformulate a problem that has secondorder cone and/or semidefiniteness constraints in order to solve it using a generalpurpose interiorpoint algorithm for nonlinear programming. The resulting problems are smooth and convex, and numerical results from the DIMAC ..."
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Cited by 11 (1 self)
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In this paper, we describe how to reformulate a problem that has secondorder cone and/or semidefiniteness constraints in order to solve it using a generalpurpose interiorpoint algorithm for nonlinear programming. The resulting problems are smooth and convex, and numerical results from the DIMACS Implementation Challenge problems and SDPLib are provided.