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E3

[1HB] Prerequisites:[1F6],[1GB],[1H8].Let f,πœ‘ be of class C2 in the open set A, and let x― be a minimum point for f constrained to Ea; let πœ† be the Lagrange multiplier; let’s define h=f(x)+πœ†πœ‘(x), then

βˆ€v,vβ‹…βˆ‡πœ‘(x)=0⟹vβ‹…Hvβ‰₯0

where H is the Hessian matrix of h.

Solution 1

[1HC]

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