IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v91y2025i2d10.1007_s10589-024-00642-z.html
   My bibliography  Save this article

Strong global convergence properties of algorithms for nonlinear symmetric cone programming

Author

Listed:
  • R. Andreani

    (University of Campinas)

  • G. Haeser

    (University of São Paulo)

  • A. Ramos

    (Universidad de Tarapacá)

  • D. O. Santos

    (Federal University of São Paulo)

  • L. D. Secchin

    (Federal University of Espírito Santo)

  • A. Serranoni

    (University of São Paulo)

Abstract

Sequential optimality conditions have played a major role in establishing strong global convergence properties of numerical algorithms for many classes of optimization problems. In particular, the way complementarity is handled defines different optimality conditions and is fundamental to achieving a strong condition. Typically, one uses the inner product structure to measure complementarity, which provides a general approach to conic optimization problems, even in the infinite-dimensional case. In this paper we exploit the Jordan algebraic structure of symmetric cones to measure complementarity, resulting in a stronger sequential optimality condition related to the well-known complementary approximate Karush-Kuhn-Tucker conditions in standard nonlinear programming. Our results improve some known results in the setting of semidefinite programming and second-order cone programming in a unified framework. In particular, we obtain global convergence that are stronger than those known for augmented Lagrangian and interior point methods for general symmetric cones.

Suggested Citation

  • R. Andreani & G. Haeser & A. Ramos & D. O. Santos & L. D. Secchin & A. Serranoni, 2025. "Strong global convergence properties of algorithms for nonlinear symmetric cone programming," Computational Optimization and Applications, Springer, vol. 91(2), pages 397-421, June.
    • Handle: RePEc:spr:coopap:v:91:y:2025:i:2:d:10.1007_s10589-024-00642-z
    DOI: 10.1007/s10589-024-00642-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-024-00642-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-024-00642-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Christian Kanzow & Andreas B. Raharja & Alexandra Schwartz, 2021. "Sequential optimality conditions for cardinality-constrained optimization problems with applications," Computational Optimization and Applications, Springer, vol. 80(1), pages 185-211, September.
    2. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    3. R. Andreani & E. H. Fukuda & G. Haeser & D. O. Santos & L. D. Secchin, 2021. "On the use of Jordan Algebras for improving global convergence of an Augmented Lagrangian method in nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 79(3), pages 633-648, July.
    4. Héctor Ramírez & David Sossa, 2017. "On the Central Paths in Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 649-668, February.
    5. Roberto Andreani & Walter Gómez & Gabriel Haeser & Leonardo M. Mito & Alberto Ramos, 2022. "On Optimality Conditions for Nonlinear Conic Programming," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 2160-2185, August.
    6. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Discussion Paper 2002-73, Tilburg University, Center for Economic Research.
    7. Bruno F. Lourenço & Ellen H. Fukuda & Masao Fukushima, 2018. "Optimality Conditions for Problems over Symmetric Cones and a Simple Augmented Lagrangian Method," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1233-1251, November.
    8. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Other publications TiSEM b25faf5d-0142-4e14-b598-a, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stefania Bellavia & Valentina Simone & Benedetta Morini, 2025. "Preface: New trends in large scale optimization," Computational Optimization and Applications, Springer, vol. 91(2), pages 351-356, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Renan W. Prado & Sandra A. Santos & Lucas E. A. Simões, 2023. "On the Fulfillment of the Complementary Approximate Karush–Kuhn–Tucker Conditions and Algorithmic Applications," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 705-736, May.
    2. Stinstra, Erwin & den Hertog, Dick, 2008. "Robust optimization using computer experiments," European Journal of Operational Research, Elsevier, vol. 191(3), pages 816-837, December.
    3. Stinstra, E., 2006. "The meta-model approach for simulation-based design optimization," Other publications TiSEM 713f828a-4716-4a19-af00-e, Tilburg University, School of Economics and Management.
    4. Anand, C. & Sotirov, R. & Terlaky, T. & Zheng, Z., 2007. "Magnetic resonance tissue density estimation using optimal SSFP pulse-sequence design," Other publications TiSEM 371b5075-1085-4bf5-bd55-4, Tilburg University, School of Economics and Management.
    5. Zohrizadeh, Fariba & Josz, Cedric & Jin, Ming & Madani, Ramtin & Lavaei, Javad & Sojoudi, Somayeh, 2020. "A survey on conic relaxations of optimal power flow problem," European Journal of Operational Research, Elsevier, vol. 287(2), pages 391-409.
    6. Stinstra, E. & den Hertog, D., 2005. "Robust Optimization Using Computer Experiments," Other publications TiSEM 69d6e378-c9f9-44e8-9602-f, Tilburg University, School of Economics and Management.
    7. Roberto Andreani & Ellen H. Fukuda & Gabriel Haeser & Daiana O. Santos & Leonardo D. Secchin, 2024. "Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 1-33, January.
    8. Appino, Riccardo Remo & González Ordiano, Jorge Ángel & Mikut, Ralf & Faulwasser, Timm & Hagenmeyer, Veit, 2018. "On the use of probabilistic forecasts in scheduling of renewable energy sources coupled to storages," Applied Energy, Elsevier, vol. 210(C), pages 1207-1218.
    9. Xinfu Liu & Zuojun Shen, 2016. "Rapid Smooth Entry Trajectory Planning for High Lift/Drag Hypersonic Glide Vehicles," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 917-943, March.
    10. Zhao, Shuaidong & Zhang, Kuilin, 2020. "A distributionally robust stochastic optimization-based model predictive control with distributionally robust chance constraints for cooperative adaptive cruise control under uncertain traffic conditi," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 144-178.
    11. Luciana Casacio & Aurelio R. L. Oliveira & Christiano Lyra, 2018. "Using groups in the splitting preconditioner computation for interior point methods," 4OR, Springer, vol. 16(4), pages 401-410, December.
    12. Bittencourt, Tiberio & Ferreira, Orizon Pereira, 2015. "Local convergence analysis of Inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 28-38.
    13. 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.
    14. de Groot, Oliver & Mazelis, Falk & Motto, Roberto & Ristiniemi, Annukka, 2021. "A toolkit for computing Constrained Optimal Policy Projections (COPPs)," Working Paper Series 2555, European Central Bank.
    15. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    16. Welington Oliveira & Valentina Sessa & David Sossa, 2024. "Computing Critical Angles Between Two Convex Cones," Journal of Optimization Theory and Applications, Springer, vol. 201(2), pages 866-898, May.
    17. Jean C. A. Medeiros & Ademir A. Ribeiro & Mael Sachine & Leonardo D. Secchin, 2025. "A Practical Second-Order Optimality Condition for Cardinality-Constrained Problems with Application to an Augmented Lagrangian Method," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-25, August.
    18. Michaël Allouche & Emmanuel Gobet & Clara Lage & Edwin Mangin, 2024. "Structured dictionary learning of rating migration matrices for credit risk modeling," Computational Statistics, Springer, vol. 39(6), pages 3431-3456, September.
    19. repec:hal:wpaper:hal-03715954 is not listed on IDEAS
    20. Enrico Bettiol & Lucas Létocart & Francesco Rinaldi & Emiliano Traversi, 2020. "A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs," Computational Optimization and Applications, Springer, vol. 75(2), pages 321-360, March.
    21. Dominik Garmatter & Margherita Porcelli & Francesco Rinaldi & Martin Stoll, 2023. "An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations," Computational Optimization and Applications, Springer, vol. 84(1), pages 191-223, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:91:y:2025:i:2:d:10.1007_s10589-024-00642-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.