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

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.


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