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- Erling D. Andersen, Knud D. Andersen
- Math. Program.
- 1995

Most modem linear programming solvers analyze the LP problem before submitting it to optimization. Some examples are the solvers WHIZARD (Tomlin and Welch, 1983), OBI (Lustig et al., 1994), OSL (Forrest and Tomlin, 1992), Sciconic (1990) and CPLEX (Bixby, 1994). The purpose of the presolve phase is to reduce the problem size and to discover whether the… (More)

- Knud D. Andersen, Edmund Christiansen, Andrew R. Conn, Michael L. Overton
- SIAM J. Scientific Computing
- 2000

The problem of minimizing a sum of Euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. We derive a primal-dual interior-point algorithm for the problem, by applying Newton’s… (More)

- Knud D. Andersen
- SIAM Journal on Optimization
- 1996

- Knud D. Andersen
- ACM Trans. Math. Softw.
- 1996

The main computational work in interior-point methods for linear programming (LP) is to solve a least-squares problem. The normal equations are often used, but if the LP constraint matrix contains a nearly dense column the normal-equations matrix will be nearly dense. Assuming that the nondense part of the constraint matrix is of full rank, the Schur… (More)

The collapse state of a rigid plastic material with the linearized Mises yield condition is computed. We use an infeasible point variant of the dual aane scaling algorithm for linear programming which is extremely eecient for this large sparse and ill conditioned problem. For a classical test problem we obtain better results than previously, both for the… (More)

The XPRESS 1 interior point optimizer is an \industrial strength" code for solution of large-scale sparse linear programs. The purpose of the present paper is to discuss how the XPRESS interior point optimizer has been parallelized for a Silicon Graphics multi processor computer. The major computational task, performed in each iteration of the… (More)

- Knud D. Andersen, Edmund Christiansen, Michael L. Overton
- SIAM J. Scientific Computing
- 1998

This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for example, the von Mises condition. After discretization with the finite element method, using divergence-free elements for the plastic flow, the kinematic formulation reduces to the problem of minimizing a sum of… (More)

- Knud D. Andersen, Edmund Christiansen
- Comp. Opt. and Appl.
- 1998

- Knud D. Andersen
- 1995

An algorithm for minimizing a sum of Euclidean Norms subject to linear equality constraints is described. The algorithm is based on a recently developed Newton barrier method for the unconstrained minimization of a sum of Euclidean norms (MSN). The linear equality constraints are handled using an exact L 1 penalty function which is made smooth in the same… (More)

- Knud D. Andersen, Edmund Christianseny, Andrew R. Connz, Michael L. Overtonx
- 1998

The problem of minimizing a sum of Euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature. This nonsmooth optimization problem arises in many diierent kinds of modern scientiic applications. We derive a primal-dual interior-point algorithm for the problem, by applying Newton's method… (More)

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