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Regularity Conditions in Vector Optimization

Author

Listed:
  • G. Bigi

    (University of Pisa)

  • M. Pappalardo

    (University of Pisa)

Abstract

By exploiting very recent results concerning linear separation between a set and a convex cone, the image space approach allows us to achieve new regularity conditions for vector minimum problems. In particular, we obtain very general Mangasarian–Fromovitz type conditions.

Suggested Citation

  • G. Bigi & M. Pappalardo, 1999. "Regularity Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 83-96, July.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:1:d:10.1023_a:1021890328184
    DOI: 10.1023/A:1021890328184
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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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. 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. 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.
    4. 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.
    5. G. Giorgi & B. Jiménez & V. Novo, 2009. "Strong Kuhn–Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 288-304, December.
    6. 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.
    7. 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.
    8. J.M. Martínez & B.F. Svaiter, 2003. "A Practical Optimality Condition Without Constraint Qualifications for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 117-133, July.

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    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. 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.
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