Properties
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The statement of the theorem
The following are useful properties of convex optimization problems:
- every point that is local minimum is also a global minimum;
- the optimal set is convex;
- 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.
- ^Rockafellar, R. Tyrrell (1993). "Lagrange multipliers and optimality"(PDF). SIAM Review. 35 (2): 183–238. Bibcode:1993SIAMR..35..183R. CiteSeerX10.1.1.161.7209. doi:10.1137/1035044.
- ^Cite error: The named reference :2 was invoked but never defined (see the help page).