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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    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. 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.
    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. 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.
    10. 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.
    11. 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.

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