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A simplified homogeneous and selfdual linear programming algorithm and its implementation
 Annals of Operations Research
, 1996
"... 1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x ..."
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Cited by 63 (5 self)
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1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x
Solving RealWorld Linear Ordering Problems . . .
, 1995
"... Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primaldual interior point method to solve the linear prog ..."
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Cited by 30 (8 self)
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Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primaldual interior point method to solve the linear programming relaxations. A point which is a good warm start for a simplexbased cutting plane algorithm is generally not a good starting point for an interior point method. Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point, which is used to help recenter when cutting planes are added. Computational results are described for some realworld problems; the algorithm appears to be competitive with a simplexbased cutting plane algorithm.
Using an Interior Point Method in a Branch and Bound Algorithm for Integer Programming.
, 1992
"... This paper describes an experimental code that has been developed to solve zeroone mixed integer linear programs. The experimental code uses a primaldual interior point method to solve the linear programming subproblems that arise in the solution of mixed integer linear programs by the branch and ..."
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Cited by 12 (7 self)
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This paper describes an experimental code that has been developed to solve zeroone mixed integer linear programs. The experimental code uses a primaldual interior point method to solve the linear programming subproblems that arise in the solution of mixed integer linear programs by the branch and bound method. Computational results for a number of test problems are provided. Introduction Mixed integer linear programming problems are often solved by branch and bound methods. Branch and bound codes, such as the ones described in [7, 11, 12], normally use the simplex algorithm to solve linear programming subproblems that arise. In this paper, we describe an experimental branch and bound code for zeroone mixed integer linear programming problems that uses an interior point method to solve the LP subproblems. This project was motivated by the observation that interior point methods tend to quickly find feasible solutions with good objective values, but take a relatively long time to ...