Question: You have an optimization problem of minimizing a nonlinear function f(x) subject to some constraints. You have found a local solution x* , with f(x*)

You have an optimization problem of minimizing a nonlinear function f(x) subject to some constraints. You have found a local solution x* , with f(x*) = 25.

(a) Suppose that f is a convex function, and the feasible set is a convex set. Is it possible to find a feasible solution x' with f(x') < 25?

(b) Suppose that f is a convex function, and the feasible set is a nonconvex set. Is it possible to find a feasible solution x' with f(x') < 25?

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