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Let f(x) be a function on Rn with continuous first-order partial derivatives and let M be a subsp...

Let f(x) be a function on Rn with continuous first-order partial derivatives and let M be a subspace of Rn. Assume that x* ∈ M.

  1. Suppose x* minimizes f(x) on M. Prove that ∇f(x*) ∈ M⊥

  2. Assume, in addition, that f(x) is convex and ∇f(x*) ∈ M⊥. Prove that x* is a global minimizer of f(x) on M.

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Solution Note tht. ach an absolote minimum in七20 chain Rylef ONI

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