In the Lagrange multiplier method, a constrained problem is reformulated as one of finding the stationary points of an unconstrained function, whereas in the penalty method, a problem with differential constraints is reformulated to one without constraints.

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In the Lagrange multiplier method, a constrained problem is reformulated as one of finding the stationary points of an unconstrained function, whereas in the penalty method, a problem with differential constraints is reformulated to one without constraints.

(a) True

(b) False

I have been asked this question by my school teacher while I was bunking the class.

Question is from Penalty in section Flows of Viscous Incompressible Fluids of Finite Element Method

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Right option is (a) True

To explain I would say: In the Lagrange multiplier method, a constrained problem is reformulated as one of finding the stationary points of the unconstrained functional  IL(v,λ)≡Iv(v)+∫ΩcλG(v)dxdy where λ(x,y) is the Lagrange multiplier. In the penalty method, a problem with differential constraints is reformulated to one without constraints.

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