TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization

Victor Magron; Jie Wang

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arXiv · 2103.00915

TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization

Victor Magron·Jie Wang

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Abstract

The Julia library TSSOS aims at helping polynomial optimizers to solve large-scale problems with sparse input data. The underlying algorithmic framework is based on exploiting correlative and term sparsity to obtain a new moment-SOS hierarchy involving potentially much smaller positive semidefinite matrices. TSSOS can be applied to numerous problems ranging from power networks to eigenvalue and trace optimization of noncommutative polynomials, involving up to tens of thousands of variables and constraints.

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Victor Magron, Jie Wang. 2021-03-01. TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization. https://arxiv.org/abs/2103.00915

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