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Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization

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  • A. Pascoletti

    (University of Udine
    CISM, International Centre for Mechanical Sciences)

  • P. Serafini

    (University of Udine
    CISM, International Centre for Mechanical Sciences)

Abstract

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints.

Suggested Citation

  • A. Pascoletti & P. Serafini, 2007. "Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 399-411, September.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:3:d:10.1007_s10957-007-9216-y
    DOI: 10.1007/s10957-007-9216-y
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    References listed on IDEAS

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    1. 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.
    2. Wan, Yieh-Hei, 1975. "On local Pareto optima," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 35-42, March.
    3. 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. 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.

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