Generalization to Several Equality Constraints

Let us derive in terms of Lagrange multipliers the necessary conditions for the 

There exists at least a pair of variations 6z and 5 2 corresponding to which the determinant 

If y is optimal, then it must satisfy the above constraints. Therefore, the first set of two necessary conditions is 

Applying the Inverse Function Theorem as before, we establish 

Because of the provision of constraint qualification, J70 0. Thus, we can introduce the Lagrange multipliers 

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