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First and Second-Order Lagrange Claims for Set-Valued Maps

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  • M. Durea

    (“Al. I. Cuza” University)

Abstract

In this note, we derive first and second-order necessary (resp. sufficient) conditions for local minimum (resp. strict local minimum) points of optimization problems governed by set-valued maps. This allows us to present and to solve a generalized Lagrange claim in a multivalued setting.

Suggested Citation

  • M. Durea, 2007. "First and Second-Order Lagrange Claims for Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 111-116, April.
    • Handle: RePEc:spr:joptap:v:133:y:2007:i:1:d:10.1007_s10957-007-9179-z
    DOI: 10.1007/s10957-007-9179-z
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    References listed on IDEAS

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    1. L Qi, 2001. "On an Extended Lagrange Claim," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 685-688, March.
    2. L. R. Huang, 2005. "Separate Necessary and Sufficient Conditions for the Local Minimum of a Function," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 241-246, April.
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    Cited by:

    1. Tenconi Paolo, 2008. "Zero variance in Markov chain Monte Carlo with an application to credit risk estimation," Economics and Quantitative Methods qf0804, Department of Economics, University of Insubria.
    2. Phan Quoc Khanh & Nguyen Minh Tung, 2016. "Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 45-69, October.

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