Projections onto the canonical simplex with additional linear inequalities
Optimization and Control
2019-11-12 v2 Numerical Analysis
Abstract
We consider the distributionally robust optimization and show that computing the distributional worst-case is equivalent to computing the projection onto the canonical simplex with additional linear inequality. We consider several distance functions to measure the distance of distributions. We write the projections as optimization problems and show that they are equivalent to finding a zero of real-valued functions. We prove that these functions possess nice properties such as monotonicity or convexity. We design optimization methods with guaranteed convergence and derive their theoretical complexity. We demonstrate that our methods have (almost) linear observed complexity.
Cite
@article{arxiv.1905.03488,
title = {Projections onto the canonical simplex with additional linear inequalities},
author = {L. Adam and V. Mácha},
journal= {arXiv preprint arXiv:1905.03488},
year = {2019}
}