COSMO: A conic operator splitting method for convex conic problems. This paper describes the Conic Operator Splitting Method (COSMO) solver, an operator splitting algorithm for convex optimisation problems with quadratic objective function and conic constraints. At each step the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. A number of benchmarks against other state-of-the-art solvers for a variety of problems show the effectiveness of our approach. Our Julia implementation is open-source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.
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References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Banjac, Goran; Lygeros, John: On the asymptotic behavior of the Douglas-Rachford and proximal-point algorithms for convex optimization (2021)
- Garstka, Michael; Cannon, Mark; Goulart, Paul: COSMO: a conic operator splitting method for convex conic problems (2021)
- Huang, Aiqun: A proximal augmented method for semidefinite programming problems (2021)
- O’Donoghue, Brendan: Operator splitting for a homogeneous embedding of the linear complementarity problem (2021)
- Rontsis, Nikitas; Osborne, Michael A.; Goulart, Paul J.: Distributionally ambiguous optimization for batch Bayesian optimization (2020)