Which of the following statements is false about convex minimization problem ?

1. AIf a local minimum exists, then it is a global minimum
2. BThe set of all global minima is convex set
3. CThe set of all global minima is concave set
4. DFor each strictly convex function, if the function has a minimum, then the minimum is unique

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Correct answer: C. The set of all global minima is concave set

Explanation

For convex problems a local minimum is global, the set of minima is convex (not concave), and a strictly convex function has at most one minimum.