An optimal adaptive algorithm for the approximation of concave functions.

Mathematical Programming (Impact Factor: 2.09). 01/2006; 107:357-366. DOI:10.1007/s10107-003-0502-7
Source: DBLP

ABSTRACT Motivated by the study of parametric convex programs, we consider approximation of concave functions by piecewise affine functions.
Using dynamic programming, we derive a procedure for selecting the knots at which an oracle provides the function value and
one supergradient. The procedure is adaptive in that the choice of a knot is dependent on the choice of the previous knots.
It is also optimal in that the approximation error, in the integral sense, is minimized in the worst case.

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J. Guérin