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2 part question.1st proof asks to show the a set of global minimizers is a convex set. 2nd proof Show that gradient at x* is 0 iff x* is a global min.
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[20 points) Suppose f(x): R” → R is a convex function. Show that the set of the global
minimizers of f(x) is a convex.
[20 points) Suppose f : R+ R is a continuously differentiable and convex function.
Show that V f (x*) = 0 iff x* is a global minimizer of f(x).
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optimization techniques
convex function
Compute the values
convex set
set of global minimizers
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