A finite algorithm for finding the projection of a point onto the canonical simplex of ∝n

By Christian Michelot. 1986

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Citations in the corpus

Parseval Networks: Improving Robustness to Adversarial Examples (2017, background): “This is a well studied problem (Michelot, 1986; Pardalos & Kovoor, 1990; Duchi et al., 2008; Condat, 2016).”
From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification (2016, background): “The Jacobian matrix of a transformation ρ , J ρ ( z ) := [ ∂ρ i ( z ) /∂z j ] i,j , is of key importance to train models with gradient-based optimization.”
Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application (2013, background): “Algorithm 1 has the advantage of being very simple, not iterative, and identifying exactly the active set at the solution after at most D steps (each of cost O (1)) after sorting.”
A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model (2013, methodology): “The projectionΠKλg ZGFN of the dual variables ξ is carioud out by simple clipping, while that of the primal variables ΠB is a projection onto the simplex in Rn (Michelot 1986).”
AD3: alternating directions dual decomposition for MAP inference in graphical models (2015, methodology): “Therefore, the AD3 subproblem for the XOR factor consists in projecting onto the probability simplex, a problem well studied in the literature (Brucker, 1984; Michelot, 1986; Duchi et al., 2008).”
Sparse Sequence-to-Sequence Models (2019, methodology): “exact, based on sorting (Held et al., 1974; Michelot, 1986),”
Optimal Resource Allocation for MIMO Ad Hoc Cognitive Radio Networks (2008, methodology): “An efficient algorithm to compute such a projection is detailed in [ 16 ].”
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging (2011, unknown): “See for example [ 20 ] for an algorithm based on successive projections and corrections.”
Advanced Structured Prediction (2014, methodology): “Projection to a simplex in (1.15) can be done e.g. by method proposed by Michelot (1986).”