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Some Notes on Approximate Optimality Conditions in Scalar and Vector Optimization Problems

Author

Listed:
  • Giorgio Giorgi

    (Department of Economics and Management, University of Pavia)

  • Bienvenido Jiménez

    (Departamento de Matematica Aplicada, E.T.S.I.I. Universidad Nacionale de Educacion a Distancia, Madrid, Spain)

  • Vicente Novo

    (Departamento de Matematica Aplicada, E.T.S.I.I. Universidad Nacionale de Educacion a Distancia, Madrid, Spain)

Abstract

We give an overview and make some remarks on the approximate optimality conditions, for a nonlinear programming problem, given by Haeser and Schuverdt (2011) and by Fiacco and McCormick (1968a). Other first-order optimality conditions in absence of constraint qualifications are examined. Finally, we extend to a Pareto problem the approximate optimality conditions of Haeser and Schuverdt.

Suggested Citation

  • Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2014. "Some Notes on Approximate Optimality Conditions in Scalar and Vector Optimization Problems," DEM Working Papers Series 095, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0095
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0095.pdf
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    References listed on IDEAS

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    1. K. O. Kortanek & J. P. Evans, 1968. "Asymptotic Lagrange Regularity for Pseudoconcave Programming with Weak Constraint Qualification," Operations Research, INFORMS, vol. 16(4), pages 849-857, August.
    2. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    3. 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.
    4. Birbil, S.I. & Frenk, J.B.G. & Still, G.J., 2007. "An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 479-484, July.
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    Cited by:

    1. 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.

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