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A fast computational algorithm for the Legendre-Fenchel transform. (English) Zbl 0852.90117
Summary: We investigate a fast algorithm, introduced by Brenier, which computes the Legendre-Fenchel transform of a real-valued function. We generalize his work to boxed domains and introduce a parameter in order to build an iterative algorithm. The new approach of separating primal and dual spaces allows a clearer understanding of the algorithm and yields better numerical behavior. We extend known complexity results and give new ones about the convergence of the algorithm.

MSC:
90C30 Nonlinear programming
49J52 Nonsmooth analysis
90C60 Abstract computational complexity for mathematical programming problems
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