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Augmented Lagrangians in semi-infinite programming

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Abstract

We consider the class of semi-infinite programming problems which became in recent years a powerful tool for the mathematical modeling of many real-life problems. In this paper, we study an augmented Lagrangian approach to semi-infinite problems and present necessary and sufficient conditions for the existence of corresponding augmented Lagrange multipliers. Furthermore, we discuss two particular cases for the augmenting function: the proximal Lagrangian and the sharp Lagrangian.

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Authors and Affiliations

  1. School of Mathematics, The University of Birmingham Edgbaston, Birmingham, B152TT, UK

    Jan-J. Rückmann

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA

    Alexander Shapiro

Authors
  1. Jan-J. Rückmann
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  2. Alexander Shapiro
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Correspondence to Alexander Shapiro.

Additional information

The work of this author was supported by CONACyT grant 44003.

The work of this author was partly supported by the NSF grant DMS-0510324.

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Rückmann, JJ., Shapiro, A. Augmented Lagrangians in semi-infinite programming. Math. Program. 116, 499–512 (2009). https://doi.org/10.1007/s10107-007-0115-7

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  • DOI: https://doi.org/10.1007/s10107-007-0115-7

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