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Regularity Conditions in Differentiable Vector Optimization Revisited

Author

Listed:
  • M. C. Maciel

    (Southern National University)

  • S. A. Santos

    (State University of Campinas)

  • G. N. Sottosanto

    (Comahue National University)

Abstract

This work is concerned with differentiable constrained vector optimization problems. It focus on the intrinsic connection between positive linearly dependent gradient sets and the distinct notions of regularity that come to play in this context. The main aspect of this contribution is the development of regularity conditions, based on the positive linear dependence or independence of gradient sets, for problems with general nonlinear constraints, without any convexity hypothesis. Being easy to verify, these conditions might be useful to define termination criteria in the development of algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:2:d:10.1007_s10957-009-9519-2
    DOI: 10.1007/s10957-009-9519-2
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    References listed on IDEAS

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    1. V. Preda & I. Chiţescu, 1999. "On Constraint Qualification in Multiobjective Optimization Problems: Semidifferentiable Case," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 417-433, February.
    2. G. Bigi & M. Pappalardo, 1998. "Regularity Conditions for the Linear Separation of Sets," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 533-540, 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. M. Castellani & G. Mastroeni & M. Pappalardo, 1997. "Separation of Sets, Lagrange Multipliers, and Totally Regular Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 249-261, February.
    5. G. Bigi & M. Pappalardo, 1999. "Regularity Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 83-96, July.
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    Citations

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    Cited by:

    1. Maria C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2016. "On the Fritz John saddle point problem for differentiable multiobjective optimization," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 917-933, December.
    2. Regina S. Burachik & M. M. Rizvi, 2012. "On Weak and Strong Kuhn–Tucker Conditions for Smooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 477-491, November.
    3. 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.
    4. Min Feng & Shengjie Li, 2018. "An approximate strong KKT condition for multiobjective optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 489-509, October.
    5. Gabriel Haeser & Alberto Ramos, 2020. "Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 469-487, November.
    6. Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.
    7. Elena Constantin, 2021. "Necessary conditions for weak minima and for strict minima of order two in nonsmooth constrained multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 177-193, May.
    8. Elena Constantin, 2020. "Second-Order Optimality Conditions in Locally Lipschitz Inequality-Constrained Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 50-67, July.

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