Operator splitting algorithm for viscoelastic flow and numerical analysis for the flow around a sphere in a tube

1996 ◽  
Vol 63 (2-3) ◽  
pp. 121-140 ◽  
Author(s):  
X.-L Luo
Keyword(s):  
Numerical Analysis ◽  
Operator Splitting ◽  
Viscoelastic Flow ◽  
Splitting Algorithm

scholarly journals COSMO: A Conic Operator Splitting Method for Convex Conic Problems

2021 ◽  
Vol 190 (3) ◽  
pp. 779-810
Author(s):  
Michael Garstka ◽  
Mark Cannon ◽  
Paul Goulart
Keyword(s):  
Convex Sets ◽  
Operator Splitting ◽  
Splitting Method ◽  
Computational Cost ◽  
Coefficient Matrix ◽  
Benchmark Problems ◽  
Portfolio Optimisation ◽  
Splitting Algorithm ◽  
Semidefinite Programs ◽  
Operator Splitting Method

AbstractThis paper describes the conic operator splitting method (COSMO) solver, an operator splitting algorithm and associated software package 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. Numerical comparisons with other state-of-the-art solvers for a variety of benchmark 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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