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Some Investigations on Saddle Points of the Lagrangian Function

Author

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  • Giorgio Giorgi

    (University of Pavia)

Abstract

We take into consideration the classical saddle points conditions of the Lagrangian function for a convex (or concave) minimization problem (maximization problem). After recalling some basic results, we give a survey of several constraint qualifications and regularity conditions assuring that the Kuhn-Tucker saddle points conditions hold. Then we discuss the existence of saddle points conditions for some classes of functions more general than the class of convex (or concave) functions. Finally, we discuss saddle points conditions for programming problems with convex (or concave) constraints, linear affine constraints and a set constraint.

Suggested Citation

  • Giorgio Giorgi, 2024. "Some Investigations on Saddle Points of the Lagrangian Function," DEM Working Papers Series 223, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0223
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    File URL: https://economiaemanagement.dip.unipv.it/sites/dip10/files/2024-10/DEMWP0223.pdf
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