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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)

Most modem linear programming solvers analyze the LP problem before submitting it to optimization. The purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible. In this paper we present a comprehensive survey of presolve methods. Moreover, we discuss the restoration procedure in detail, i.e.,… (More)

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)

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)

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)

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 Andersen
- 1999

Making an optimal choice, given a number of possibilities and constraints, is a fundamental problem in economics and engineering. Examples include the optimal choice of a portfolio of stocks, given a budget and diversity requirements; the optimal design of a truss, given certain load requirements; and the determination of an optimal production plan, given… (More)