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Metric regularity, tangent sets, and second-order optimality conditions

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Abstract

A strong regularity theorem is proved, which shows that the usual constraint qualification conditions ensuring the regularity of the set-valued maps expressing feasibility in optimization problems, are in fact minimal assumptions. These results are then used to derive calculus rules for second-order tangent sets, allowing us in turn to obtain a second-order (Lagrangian) necessary condition for optimality which completes the usual one of positive semidefiniteness on the Hessian of the Lagrangian function.

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Authors and Affiliations

  1. Département de Mathématiques Appliquées, Université Blaise Pascal (Clermont II), BP 45, 63170, Aubière, France

    Roberto Cominetti

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  1. Roberto Cominetti
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Communicated by J. Stoer

On leave from Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile.

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Cominetti, R. Metric regularity, tangent sets, and second-order optimality conditions. Appl Math Optim 21, 265–287 (1990). https://doi.org/10.1007/BF01445166

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