SparseCoLO (Conversion Methods for SPARSE COnic-form Linear Optimization). SparseCoLO is a Matlab package for implementing the four conversion methods, proposed by Kim, Kojima, Mevissen and Yamashita, via positive semidefinite matrix completion for an optimization problem with matrix inequalities satisfying a sparse chordal graph structure. It is based on quite a general description of optimization problem including both primal and dual form of linear, semidefinite, second-order cone programs with equality/inequality constraints. Among the four conversion methods, two methods utilize the domain-space sparsity of a semidefinite matrix variable and the other two methods the range-space sparsity of a linear matrix inequality (LMI) constraint of the given problem. SparseCoLO can be used as a preprocessor to reduce the size of the given problem before applying semidefinite programming solvers.

References in zbMATH (referenced in 12 articles )

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  1. Arslan, Ali; Fantuzzi, Giovanni; Craske, John; Wynn, Andrew: Bounds on heat transport for convection driven by internal heating (2021)
  2. Garstka, Michael; Cannon, Mark; Goulart, Paul: COSMO: a conic operator splitting method for convex conic problems (2021)
  3. Kočvara, Michal: Decomposition of arrow type positive semidefinite matrices with application to topology optimization (2021)
  4. Zhang, Richard Y.; Lavaei, Javad: Sparse semidefinite programs with guaranteed near-linear time complexity via dualized clique tree conversion (2021)
  5. Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan: Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures (2020)
  6. Zheng, Yang; Fantuzzi, Giovanni; Papachristodoulou, Antonis; Goulart, Paul; Wynn, Andrew: Chordal decomposition in operator-splitting methods for sparse semidefinite programs (2020)
  7. Fantuzzi, Giovanni; Pershin, Anton; Wynn, Andrew: Bounds on heat transfer for Bénard-Marangoni convection at infinite Prandtl number (2018)
  8. Kim, Sunyoung; Kojima, Masakazu: Binary quadratic optimization problems that are difficult to solve by conic relaxations (2017)
  9. Kojima, Masakazu; Yamashita, Makoto: Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization (2013)
  10. Kim, Sunyoung; Kojima, Masakazu; Mevissen, Martin; Yamashita, Makoto: Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion (2011)
  11. Kojima, Masakazu: Exploiting structured sparsity in large scale semidefinite programming problems (2010)
  12. Zhu, Zhisu; So, Anthony Man-Cho; Ye, Yinyu: Universal rigidity and edge sparsification for sensor network localization (2010)