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Matrix-free interior point method

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  • Jacek Gondzio, 2012. "Matrix-free interior point method," Computational Optimization and Applications, Springer, vol. 51(2), pages 457-480, March.
    • Handle: RePEc:spr:coopap:v:51:y:2012:i:2:p:457-480
    DOI: 10.1007/s10589-010-9361-3
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    1. S. Bellavia, 1998. "Inexact Interior-Point Method," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 109-121, January.
    2. Luca Bergamaschi & Jacek Gondzio & Manolo Venturin & Giovanni Zilli, 2007. "Inexact constraint preconditioners for linear systems arising in interior point methods," Computational Optimization and Applications, Springer, vol. 36(2), pages 137-147, April.
    3. G. Al-Jeiroudi & J. Gondzio, 2009. "Convergence Analysis of the Inexact Infeasible Interior-Point Method for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 231-247, May.
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    Cited by:

    1. Gondzio, Jacek, 2016. "Crash start of interior point methods," European Journal of Operational Research, Elsevier, vol. 255(1), pages 308-314.
    2. Cecilia Orellana Castro & Manolo Rodriguez Heredia & Aurelio R. L. Oliveira, 2023. "Recycling basic columns of the splitting preconditioner in interior point methods," Computational Optimization and Applications, Springer, vol. 86(1), pages 49-78, September.
    3. Kimon Fountoulakis & Jacek Gondzio, 2016. "Performance of first- and second-order methods for $$\ell _1$$ ℓ 1 -regularized least squares problems," Computational Optimization and Applications, Springer, vol. 65(3), pages 605-635, December.
    4. Sebastiaan Breedveld & Bas Berg & Ben Heijmen, 2017. "An interior-point implementation developed and tuned for radiation therapy treatment planning," Computational Optimization and Applications, Springer, vol. 68(2), pages 209-242, November.
    5. Songqiang Qiu, 2019. "Convergence of a stabilized SQP method for equality constrained optimization," Computational Optimization and Applications, Springer, vol. 73(3), pages 957-996, July.
    6. Manolo Rodriguez Heredia & Aurelio Ribeiro Leite Oliveira, 2020. "A new proposal to improve the early iterations in the interior point method," Annals of Operations Research, Springer, vol. 287(1), pages 185-208, April.
    7. Yiran Cui & Keiichi Morikuni & Takashi Tsuchiya & Ken Hayami, 2019. "Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning," Computational Optimization and Applications, Springer, vol. 74(1), pages 143-176, September.
    8. J. Gondzio & F. N. C. Sobral, 2019. "Quasi-Newton approaches to interior point methods for quadratic problems," Computational Optimization and Applications, Springer, vol. 74(1), pages 93-120, September.
    9. Stefano Cipolla & Jacek Gondzio, 2023. "Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1061-1103, June.
    10. Filippo Zanetti & Jacek Gondzio, 2023. "An Interior Point–Inspired Algorithm for Linear Programs Arising in Discrete Optimal Transport," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1061-1078, September.
    11. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    12. Ploskas, Nikolaos & Samaras, Nikolaos, 2015. "Efficient GPU-based implementations of simplex type algorithms," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 552-570.
    13. Bethany L. Nicholson & Wei Wan & Shivakumar Kameswaran & Lorenz T. Biegler, 2018. "Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 70(2), pages 321-350, June.
    14. Stefania Bellavia & Valentina De Simone & Daniela di Serafino & Benedetta Morini, 2016. "On the update of constraint preconditioners for regularized KKT systems," Computational Optimization and Applications, Springer, vol. 65(2), pages 339-360, November.

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