Question 7882 – Computer-Networks
January 26, 2024Question 597 – ISRO CS 2013
January 26, 2024Question 5249 – Minimization-Problem
Which of the following statements is false about convex minimization problem ?
Correct Answer: C
Question 1 Explanation:
Properties of convex optimization problems:
1. Every local minimum is a global minimum
2. The optimal set is convex
3. If the objective function is strictly convex, then the problem has at most one optimal point.
These results are used by the theory of convex minimization along with geometric notions from functional analysis (in Hilbert spaces) such as the Hilbert projection theorem, the separating hyperplane theorem, and Farkas’ lemma.
1. Every local minimum is a global minimum
2. The optimal set is convex
3. If the objective function is strictly convex, then the problem has at most one optimal point.
These results are used by the theory of convex minimization along with geometric notions from functional analysis (in Hilbert spaces) such as the Hilbert projection theorem, the separating hyperplane theorem, and Farkas’ lemma.
If a local minimum exists, then it is a global minimum
The set of all global minima is convex set
The set of all global minima is concave set
For each strictly convex function, if the function has a minimum, then the minimum is unique
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