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- W2094241350 abstract "A geometrically convergent algorithm is presented to determine min ∥ƒ(2)∥∞, where ƒ interpolates the given p points {(xi, yi)}1p with increasing xi's, ƒ ϵ C1, ƒ is absolutely continuous, ƒ(2) ϵ L∞[x1, xp], and ƒ satisfies the additional constraint of being convex. Starting with an easily available lower bound K, it determines an upper bound K̄ and then successively reduces the difference |K−K| to the desired level of accuracy. For the given K,K and an error tolerance level ε > 0, n iterations, where n is the smallest integer ⩾(ln[ε/(|K − K|)]/ln(0.5)), will determine a k with ¦k − k∗¦ ⩽ ε, where k∗ is the optimal value of ∥ƒ(2)∥∞. For clarification, a numerical example and results of an initial computer implementation for p = 5, 15, 50, 75, 100, are given. These results suggest the algorithm to be fast and capable of solving problems with large values of p. Moreover, the general approach underlying the algorithm would seem to be applicable to other related problems." @default.
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- W2094241350 date "1991-02-01" @default.
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- W2094241350 title "Constrained optimization in L∞-norm: An algorithm for convex quadratic interpolation" @default.
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- W2094241350 doi "https://doi.org/10.1016/0022-247x(91)90036-y" @default.
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