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Geometry of optimality conditions and constraint qualifications

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Abstract

Certain types of necessary optimality conditions for mathematical programming problems are equivalent to corresponding regularity conditions on the constraint set. For any problem, a certain natural optimality condition, dependent upon the particular constraint set, is always satisfied. This condition can be strengthened in numerous ways by invoking appropriate regularity assumptions on the constraint set. Results are presented for Euclidean spaces and some extensions to Banach spaces are given.

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Authors and Affiliations

  1. University of North Carolina, Chapel Hill, North Carolina, USA

    F. J. Gould & Jon W. Tolle

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  1. F. J. Gould
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  2. Jon W. Tolle
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Additional information

This work was supported in part by the Office of Naval Research, Contract No. N00014-67-A-0321-0003 (NR-047-095).

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Gould, F.J., Tolle, J.W. Geometry of optimality conditions and constraint qualifications. Mathematical Programming 2, 1–18 (1972). https://doi.org/10.1007/BF01584534

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  • DOI: https://doi.org/10.1007/BF01584534

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