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Interiorpoint Methods
, 2000
"... The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadrati ..."
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Cited by 612 (15 self)
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The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semidefinite programming, and nonconvex and nonlinear problems, have reached varying levels of maturity. We review some of the key developments in the area, including comments on both the complexity theory and practical algorithms for linear programming, semidefinite programming, monotone linear complementarity, and convex programming over sets that can be characterized by selfconcordant barrier functions.
A PrimalDual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix
, 1995
"... We propose a primaldual "layeredstep " interior point (LIP) algorithm for linear programming with data given by real numbers. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares " (LLS) ste ..."
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Cited by 57 (8 self)
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We propose a primaldual &quot;layeredstep &quot; interior point (LIP) algorithm for linear programming with data given by real numbers. This algorithm follows the central path, either with short steps or with a new type of step called a &quot;layered least squares &quot; (LLS) step. The algorithm returns an exact optimum after a finite number of stepsin particular, after O(n3:5c(A)) iterations, where c(A) is a function of the
Combining InteriorPoint and Pivoting Algorithms for Linear Programming
 Management Science
, 1996
"... ..."
Progress in Linear Programming: InteriorPoint Algorithms
, 1994
"... According to current estimates, more than $100 million in human and computer time is invested yearly in the formulation and solution of linear programming problems. Businesses, large and small, use linear programming models to optimize communication systems, to schedule transportation networks, to ..."
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According to current estimates, more than $100 million in human and computer time is invested yearly in the formulation and solution of linear programming problems. Businesses, large and small, use linear programming models to optimize communication systems, to schedule transportation networks, to control inventories, to plan investments, and to maximize production.... In this article we describe some recent developments in linear programming. We highlight progress in interiorpoint algorithms during the last ten years.