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 → ∞ 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). ©1996 Plenum Publishing Corporation.

Algorithms for approximate calculation of the minimum of a convex function from its values

Protasov, Vladimir
1996-01-01

Abstract

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 → ∞ 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). ©1996 Plenum Publishing Corporation.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/123671
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