Abstract
The paper deals with a numerical minimization problem for a convex function defined on a convexn-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 asn → ∞ is considerably less than that of similar algorithms known to the author. In fact, the complexity is improved fromCn 7 ln2(n+1) [4] toCn 2 ln(n+1).
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Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 95–102, January, 1996.
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Protasov, V.Y. Algorithms for approximate calculation of the minimum of a convex function from its values. Math Notes 59, 69–74 (1996). https://doi.org/10.1007/BF02312467
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DOI: https://doi.org/10.1007/BF02312467