Abstract
We present a unified description of a class of restart fixed point algorithms including Merrill's method and several variable dimension algorithms for their implementation on computers. Based on this description we show that some pivot-saving techniques originally developed for the homotopy methods can be applied to the class. We also propose a new variable dimension algorithm having 3n-1 rays along which we can move toward a solution. Some numerical comparisons of the simplicial restart algorithms, Merrill's method, the 2n-method, the octahedral method and the new one, support that the latter two methods are more efficient than the others.
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Kojima, M., Yamamoto, Y. A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm. Mathematical Programming 28, 288–328 (1984). https://doi.org/10.1007/BF02612336
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DOI: https://doi.org/10.1007/BF02612336