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Exponential lower bounds for finding Brouwer fixed points

1987
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28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
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The computation of Brouwer fixed points is a central tool in economic modeling. Although there have been several algorithms for computing a fixed point of a Brouwer map, starting with Scarf's algorithm of 1965, the question of worst-case complexity was not addressed. It has been conjectured that Scarf's algorithm has typical behavior that is polynomial in the dimension. Here we show that any algorithm for computing the Brouwer fixed point of a function based on function evaluations (a class

doi:10.1109/sfcs.1987.24
dblp:conf/focs/HirschV87
fatcat:k7qtmxsycjdfxgclr75m5vf2iq