A linear-time median-finding algorithm for projecting a vector on the simplex of $${\mathbb{R}}^ n$$.(English)Zbl 0679.90054

An algorithm is given for the projection of a vector $$\bar x\in R^ n$$ on the simplex $$\{x\in R^ n|$$ $$e^ Tx=1$$, $$x\geq 0\}$$. The problem is written as a convex quadratic programming problem, for which the Kuhn- Tucker conditions are solved. It is shown that the complexity is O(n) time. A numerical example is given.
Reviewer: M.A.Hanson

MSC:

 90C30 Nonlinear programming 68Q25 Analysis of algorithms and problem complexity 90C20 Quadratic programming 90C25 Convex programming
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References:

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