Geodesic
Algorithms for approximate calculation of the minimum of a~convex function from its values
Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 95-102

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The paper deals with a numerical minimization problem for a convex function defined on a convex $n$-dimensional domain and continuous (but not necessarily smooth). The values of the function can be calculated at any given point. It is required to find the minimum with desired accuracy. A new algorithm for solving this problem is presented, whose computational complexity as $n\to\infty$ is considerably less than that of similar algorithms known to the author. In fact, the complexity is improved from $Cn^7\ln^2(n+1)$ [4] to $Cn^2\ln(n+1)$. 
@article{MZM_1996_59_1_a8,
     author = {V. Yu. Protasov},
     title = {Algorithms for approximate calculation of the minimum of a~convex function from its values},
     journal = {Matemati\v{c}eskie zametki},
     pages = {95--102},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_1_a8/}
}
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V. Yu. Protasov. Algorithms for approximate calculation of the minimum of a~convex function from its values. Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 95-102. http://geodesic.mathdoc.fr/item/MZM_1996_59_1_a8/