IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v146y2010i2d10.1007_s10957-010-9671-8.html
   My bibliography  Save this article

Constant-Rank Condition and Second-Order Constraint Qualification

Author

Listed:
  • R. Andreani

    (University of Campinas)

  • C. E. Echagüe

    (University of La Plata)

  • M. L. Schuverdt

    (University of La Plata)

Abstract

The constant-rank condition for feasible points of nonlinear programming problems was defined by Janin (Math. Program. Study 21:127–138, 1984). In that paper, the author proved that the constant-rank condition is a first-order constraint qualification. In this work, we prove that the constant-rank condition is also a second-order constraint qualification. We define other second-order constraint qualifications.

Suggested Citation

  • R. Andreani & C. E. Echagüe & M. L. Schuverdt, 2010. "Constant-Rank Condition and Second-Order Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 255-266, August.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9671-8
    DOI: 10.1007/s10957-010-9671-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9671-8
    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/s10957-010-9671-8?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 search for a different version of it.

    References listed on IDEAS

    as
    1. A. Baccari, 2004. "On the Classical Necessary Second-Order Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 213-221, October.
    2. Stephen Wright & Daniel Ralph, 1996. "A Superlinear Infeasible-Interior-Point Algorithm for Monotone Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 815-838, November.
    3. R. Andreani & J. M. Martinez & M. L. Schuverdt, 2005. "On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 473-483, May.
    4. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 147-163, July.
    5. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 165-183, July.
    6. D.P. Bertsekas & A.E. Ozdaglar, 2002. "Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 287-343, August.
    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. Iasson Karafyllis, 2014. "Feedback Stabilization Methods for the Solution of Nonlinear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 783-806, June.
    2. Roger Behling & Gabriel Haeser & Alberto Ramos & Daiana S. Viana, 2018. "On a Conjecture in Second-Order Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 625-633, March.
    3. Roberto Andreani & Gabriel Haeser & Leonardo M. Mito & C. Héctor Ramírez & Thiago P. Silveira, 2022. "Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 42-78, October.
    4. Kaiwen Meng & Xiaoqi Yang, 2015. "First- and Second-Order Necessary Conditions Via Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 720-752, June.
    5. María C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2011. "On Second-Order Optimality Conditions for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 332-351, May.
    6. Giorgio Giorgi, 2019. "Notes on Constraint Qualifications for Second-Order Optimality Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(5), pages 16-32, October.
    7. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    8. Kuang Bai & Yixia Song & Jin Zhang, 2023. "Second-Order Enhanced Optimality Conditions and Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1264-1284, September.
    9. Lei Guo & Gui-Hua Lin & Jane J. Ye, 2013. "Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 33-64, July.
    10. Giorgio Giorgi, 2018. "A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions," DEM Working Papers Series 160, University of Pavia, Department of Economics and Management.
    11. Min Feng & Shengjie Li, 2019. "Second-Order Strong Karush/Kuhn–Tucker Conditions for Proper Efficiencies in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 766-786, 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. Leonid Minchenko, 2019. "Note on Mangasarian–Fromovitz-Like Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1199-1204, September.
    2. L. Minchenko & A. Tarakanov, 2011. "On Error Bounds for Quasinormal Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 571-579, March.
    3. Nguyen Huy Chieu & Gue Myung Lee, 2014. "Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and their Local Preservation Property," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 755-776, December.
    4. Giorgio Giorgi, 2018. "A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions," DEM Working Papers Series 160, University of Pavia, Department of Economics and Management.
    5. Gabriel Haeser & María Laura Schuverdt, 2011. "On Approximate KKT Condition and its Extension to Continuous Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 528-539, June.
    6. María C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2011. "On Second-Order Optimality Conditions for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 332-351, May.
    7. Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
    8. Kuang Bai & Yixia Song & Jin Zhang, 2023. "Second-Order Enhanced Optimality Conditions and Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1264-1284, September.
    9. Letizia Pellegrini & Shengkun Zhu, 2018. "Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part II: The Vector Finite-Dimensional Case," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 788-810, June.
    10. M. Alavi Hejazi & N. Movahedian & S. Nobakhtian, 2018. "On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 778-799, December.
    11. S. J. Li & Y. D. Xu & S. K. Zhu, 2012. "Nonlinear Separation Approach to Constrained Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 842-856, September.
    12. Lei Guo & Gui-Hua Lin, 2013. "Notes on Some Constraint Qualifications for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 600-616, March.
    13. Y. D. Xu & S. J. Li, 2013. "Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 663-684, June.
    14. Satoshi Suzuki & Daishi Kuroiwa, 2012. "Necessary and Sufficient Constraint Qualification for Surrogate Duality," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 366-377, February.
    15. Olga Brezhneva & Alexey A. Tret’yakov, 2017. "When the Karush–Kuhn–Tucker Theorem Fails: Constraint Qualifications and Higher-Order Optimality Conditions for Degenerate Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 367-387, August.
    16. Satoshi Suzuki & Daishi Kuroiwa, 2011. "On Set Containment Characterization and Constraint Qualification for Quasiconvex Programming," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 554-563, June.
    17. Stephan Dempe & Alain B. Zemkoho, 2011. "The Generalized Mangasarian-Fromowitz Constraint Qualification and Optimality Conditions for Bilevel Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 46-68, January.
    18. Hui Hu & Qing Wang, 2011. "Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 52-64, July.
    19. Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.
    20. Shengkun Zhu, 2018. "Image Space Analysis to Lagrange-Type Duality for Constrained Vector Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 743-769, June.

    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:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9671-8. 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.