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A simple constraint qualification in convex programming

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Abstract

We introduce and characterize a class of differentiable convex functions for which the Karush—Kuhn—Tucker condition is necessary for optimality. If some constraints do not belong to this class, then the characterization of optimality generally assumes an asymptotic form.

We also show that for the functions that belong to this class in multi-objective optimization, Pareto solutions coincide with strong Pareto solutions,. This extends a result, well known for the linear case.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, H3A 2K6, Montreal, Que., Canada

    X. Zhou, F. Sharifi Mokhtarian & S. Zlobec

Authors
  1. X. Zhou
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  2. F. Sharifi Mokhtarian
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  3. S. Zlobec
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Additional information

Research partly supported by the National Research Council of Canada.

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Zhou, X., Sharifi Mokhtarian, F. & Zlobec, S. A simple constraint qualification in convex programming. Mathematical Programming 61, 385–397 (1993). https://doi.org/10.1007/BF01582159

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  • DOI: https://doi.org/10.1007/BF01582159

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