Theorem Consider an optimization problem min f (x) s.t. x en where f is a convex function and 0 is a convex set: Then, every local minimum is also a global minimum. Prove the given theorem.
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Let $x^*$ be a local minimum of the optimization problem, i.e., $f(x^*) \leq f(x)$ for all $x$ in a neighborhood of $x^*$ within the set $\Omega$. Show more…
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