Lagrange multiplier approach to variational problems and applications.

*(English)*Zbl 1156.49002
Advances in Design and Control 15. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-49-8/pbk; 978-0-89871-861-4/ebook). xvi, 341 p. (2008).

In this interesting monographical book infinite-dimensional analysis is used to study in a comprehensive way Lagrange multiplier approach to nonlinear variational problems with equality and (with help of cones) inequality constraints. The contents of the book can be characterized by three intimately connected points:

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- Existence of Lagrange multipliers and sensitivity analysis (including convex analysis),
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- Computational methods and their behaviour for different classes of the considered variational problems,
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- Profound examples, which fit in the framework of both the first points.

Reviewer: Alfred Göpfert (Halle)

##### MSC:

49-02 | Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control |

49J27 | Existence theories for problems in abstract spaces |

49K27 | Optimality conditions for problems in abstract spaces |

49K40 | Sensitivity, stability, well-posedness |

49M30 | Other numerical methods in calculus of variations (MSC2010) |

49M37 | Numerical methods based on nonlinear programming |

49N15 | Duality theory (optimization) |

90C48 | Programming in abstract spaces |