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A Newton barrier method for minimizing a
sum of Euclidean norms subject to linear equality constraints

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Knud D. Andersen and Edmund Christiansen

An algorithm for minimizing a sum of Euclidean Norms subject to linear
equality constraints is described. The algorithm is based on the
Newton barrier method developed of Andersen 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 way as the Euclidean norms.
The dual problem is to maximize a linear objective function subject to
homogeneous linear equality constraints and quadratic inequalities. Hence the
suggested method also solves such problems efficiently. In fact such a
problem from plastic collapse analysis motivated this work. Numerical results
are presented for large sparse problems.
Preprint 95-07, Department of Mathematics and Computer Science,
Odense University, Denmark. February, 1995.