Theory
The following statements are true about the convex minimization problem:
- if a local minimum exists, then it is a global minimum.
- the set of all (global) minima is convex.
- for each strictly convex function, if the function has a minimum, then the minimum is unique.
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.
Read more about this topic: Convex Optimization
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