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Outer approximations are a well known technique for solving semi-infinite optimization problems. We show that a straightforward adaptation of this technique results in a new, external, active-set strategy that can easily be added to existing software packages for solving nonlinear programming problems with a large number of inequality constraints. As our numerical results show, the effect of this external active-set strategy can be spectacular, with reductions in computing time by a factor that can exceed 500.

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