Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones We describe an implementation of nonsymmetric interior-point methods for linear cone programs defined by two types of matrix cones: the cone of positive semidefinite matrices with a given chordal sparsity pattern and its dual cone, the cone of chordal sparse matrices that have a positive semidefinite completion. The implementation takes advantage of fast recursive algorithms for evaluating the function values and derivatives of the logarithmic barrier functions for these cones. We present experimental results of two implementations, one of which is based on an augmented system approach, and a comparison with publicly available interior-point solvers for semidefinite programming.
Keywords for this software
References in zbMATH (referenced in 7 articles )
Showing results 1 to 7 of 7.
- Garstka, Michael; Cannon, Mark; Goulart, Paul: COSMO: a conic operator splitting method for convex conic problems (2021)
- Liberti, Leo; Poirion, Pierre-Louis; Vu, Ky: Random projections for conic programs (2021)
- Zhang, Richard Y.; Lavaei, Javad: Sparse semidefinite programs with guaranteed near-linear time complexity via dualized clique tree conversion (2021)
- Zheng, Yang; Fantuzzi, Giovanni; Papachristodoulou, Antonis; Goulart, Paul; Wynn, Andrew: Chordal decomposition in operator-splitting methods for sparse semidefinite programs (2020)
- Friedlander, Michael P.; Goh, Gabriel: Efficient evaluation of scaled proximal operators (2017)
- Mittelmann, Hans D.: The state-of-the-art in conic optimization software (2012)
- Andersen, Martin S.; Dahl, Joachim; Vandenberghe, Lieven: Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones (2010)