OSQP: An Operator Splitting Solver for Quadratic Programs. We present a general purpose solver for quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the same coefficient matrix in each iteration. Our algorithm is very robust, placing no requirements on the problem data such as positive definiteness of the objective function or linear independence of the constraint functions. It is division-free once an initial matrix factorization is carried out, making it suitable for real-time applications in embedded systems. In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates. The method also supports factorization caching and warm starting, making it particularly efficient when solving parametrized problems arising in finance, control, and machine learning. Our open-source C implementation OSQP has a small footprint, is library-free, and has been extensively tested on many problem instances from a wide variety of application areas. It is typically ten times faster than competing interior point methods, and sometimes much more when factorization caching or warm start is used.

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. De Marchi, Alberto: On a primal-dual Newton proximal method for convex quadratic programs (2022)
  2. Li, Xiaoyue; Uysal, A. Sinem; Mulvey, John M.: Multi-period portfolio optimization using model predictive control with mean-variance and risk parity frameworks (2022)
  3. Rontsis, Nikitas; Goulart, Paul; Nakatsukasa, Yuji: Efficient semidefinite programming with approximate ADMM (2022)
  4. Verschueren, Robin; Frison, Gianluca; Kouzoupis, Dimitris; Frey, Jonathan; van Duijkeren, Niels; Zanelli, Andrea; Novoselnik, Branimir; Albin, Thivaharan; Quirynen, Rien; Diehl, Moritz: \textttacados-- a modular open-source framework for fast embedded optimal control (2022)
  5. Wu, Xiaofei; Liang, Rongmei; Yang, Hu: Penalized and constrained LAD estimation in fixed and high dimension (2022)
  6. Banjac, Goran; Lygeros, John: On the asymptotic behavior of the Douglas-Rachford and proximal-point algorithms for convex optimization (2021)
  7. Barratt, Shane; Angeris, Guillermo; Boyd, Stephen: Optimal representative sample weighting (2021)
  8. Garstka, Michael; Cannon, Mark; Goulart, Paul: COSMO: a conic operator splitting method for convex conic problems (2021)
  9. Huang, Aiqun: A proximal augmented method for semidefinite programming problems (2021)
  10. Mihić, Krešimir; Zhu, Mingxi; Ye, Yinyu: Managing randomization in the multi-block alternating direction method of multipliers for quadratic optimization (2021)
  11. Moehle, Nicholas; Kochenderfer, Mykel J.; Boyd, Stephen; Ang, Andrew: Tax-aware portfolio construction via convex optimization (2021)
  12. O’Donoghue, Brendan: Operator splitting for a homogeneous embedding of the linear complementarity problem (2021)
  13. Robert Andrew Martin: PyPortfolioOpt: portfolio optimization in Python (2021) not zbMATH
  14. Stöckel, Andreas; Eliasmith, Chris: Passive nonlinear dendritic interactions as a computational resource in spiking neural networks (2021)
  15. Bartels, Sören; Wachsmuth, Gerd: Numerical approximation of optimal convex shapes (2020)
  16. Budninskiy, Max; Abdelaziz, Ameera; Tong, Yiying; Desbrun, Mathieu: Laplacian-optimized diffusion for semi-supervised learning (2020)
  17. Fu, Anqi; Zhang, Junzi; Boyd, Stephen: Anderson accelerated Douglas-Rachford splitting (2020)
  18. Liao-McPherson, Dominic; Kolmanovsky, Ilya: FBstab: a proximally stabilized semismooth algorithm for convex quadratic programming (2020)
  19. Stellato, Bartolomeo; Banjac, Goran; Goulart, Paul; Bemporad, Alberto; Boyd, Stephen: OSQP: an operator splitting solver for quadratic programs (2020)
  20. Yue Jiang, Wolfgang Stuerzlinger, Matthias Zwicker, Christof Lutteroth: ORCSolver: An Efficient Solver for Adaptive GUI Layout with OR-Constraints (2020) arXiv

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