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TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization
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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.
Forward citations
Cited by 3 Pith papers
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Global Contact-Rich Planning with Sparsity-Rich Semidefinite Relaxations
Sparse semidefinite relaxations, exploiting correlative, term, and robotics-specific sparsity, solve contact-rich planning problems to certified near-global optimality in seconds for several benchmark tasks.
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Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
A moment-SOS semidefinite hierarchy computes best W2 and TV mixture approximations over semi-algebraic parameter sets and can recover the mixture order from a rank condition.
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An ideal-sparse generalized moment problem reformulation for completely positive tensor decomposition exploiting maximal cliques of multi-hypergraphs
The paper reformulates completely positive tensor decomposition using maximal cliques of multi-hypergraphs, yielding an ideal-sparse moment hierarchy that is much faster than dense relaxations and provably equivalent.
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