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On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification

Author

Listed:
  • R. Andreani

    (Associate Professor, IMECC-UNICAMP)

  • J. M. Martinez

    (Professor, IMECC-UNICAMP)

  • M. L. Schuverdt

    (PhD Student,IMECC-UNICAMP)

Abstract

The constant positive linear dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei (Ref. 1) and used in the analysis of SQP methods. In that paper, the authors conjectured that the CPLD could be a constraint qualification. This conjecture is proven in the present paper. Moreover, it is shown that the CPLD condition implies the quasinormality constraint qualification, but that the reciprocal is not true. Relations with other constraint qualifications are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:2:d:10.1007_s10957-004-1861-9
    DOI: 10.1007/s10957-004-1861-9
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Shuai Liu, 2019. "A simple version of bundle method with linear programming," Computational Optimization and Applications, Springer, vol. 72(2), pages 391-412, March.
    2. M. C. Maciel & S. A. Santos & G. N. Sottosanto, 2009. "Regularity Conditions in Differentiable Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 385-398, August.
    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. L. F. Bueno & G. Haeser & F. Lara & F. N. Rojas, 2020. "An Augmented Lagrangian method for quasi-equilibrium problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 737-766, July.
    5. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2016. "Approximate Karush–Kuhn–Tucker Condition in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 70-89, October.
    6. Jane J. Ye & Jin Zhang, 2014. "Enhanced Karush–Kuhn–Tucker Conditions for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 777-794, December.
    7. Christian Kanzow & Andreas B. Raharja & Alexandra Schwartz, 2021. "An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 793-813, June.
    8. Leonid Minchenko, 2019. "Note on Mangasarian–Fromovitz-Like Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1199-1204, September.
    9. Chungen Shen & Lei-Hong Zhang & Bo Wang & Wenqiong Shao, 2014. "Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 435-473, December.
    10. 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.
    11. L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Andrea Cristofari & Gianni Di Pillo & Giampaolo Liuzzi & Stefano Lucidi, 2022. "An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 300-323, June.
    17. 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.
    18. 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.
    19. Chungen Shen & Lei-Hong Zhang & Wei Liu, 2016. "A stabilized filter SQP algorithm for nonlinear programming," Journal of Global Optimization, Springer, vol. 65(4), pages 677-708, August.
    20. Mengwei Xu & Jane J. Ye, 2020. "Relaxed constant positive linear dependence constraint qualification and its application to bilevel programs," Journal of Global Optimization, Springer, vol. 78(1), pages 181-205, September.

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