# From the simplex to the sphere: Faster constrained optimization using the Hadamard parametrization

@inproceedings{Li2021FromTS, title={From the simplex to the sphere: Faster constrained optimization using the Hadamard parametrization}, author={Qiuwei Li and Daniel Mckenzie and Wotao Yin}, year={2021} }

The standard simplex in R n , also known as the probability simplex, is the set of nonnegative vectors whose entries sum up to 1. They frequently appear as constraints in optimization problems that arise in machine learning, statistics, data science, operations research, and beyond. We convert the standard simplex to the unit sphere and thus transform the corresponding constrained optimization problem into an optimization problem on a simple, smooth manifold. We show that KKT points and strict…

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