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Constrained Minimization using Lagrange Multipliers

Please see attached PDF file; I'm trying to derive a couple of results involving Lagrange multipliers and a linear algebra equivalence.

This makes use of the extension to Lagrange multipliers whereby the constraint is an inequality (see, e.g., section 5.1 of http://www.cs.berkeley.edu/~klein/papers/lagrange-multipliers.pdf ).

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