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Mathematics · L4 · Multivariable optimization pipeline

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Concept map from partial derivatives through the gradient to unconstrained critical-point classification and Lagrange-multiplier constrained optimization.

by @openstemUpdated Mathematics
f(x, y)Partial derivativesfₓ, fᵧGradient ∇f = (fₓ, fᵧ)∇f = 0?Second-derivative testD = fₓₓfᵧᵧ − (fₓᵧ)²Classify: min / max / saddleConstraint g(x,y) = c?Lagrange multipliers∇f = λ∇gYesYes

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