Abstract
A brief review is made of those basic aspects of the theory of mathematical programming which are of most relevance in the mathematical description of the theory of structures with plastic constitutive laws. Firstly, the classical problem of optimisation is used to introduce the method of Lagrange multipliers. The same method is then applied to a mathematical program with inequality constraints, and the necessary optimality criteria of Karush, Kuhn and Tucker are obtained. With the imposition of convexity, the concept of duality in mathematical programming is described, and the solutions of the consequent dual mathematical programs are related to the saddlepoint property of the associated Lagrange function.
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© 1990 Springer-Verlag Wien
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Smith, D.L. (1990). Mathematical Programming. In: Smith, D.L. (eds) Mathematical Programming Methods in Structural Plasticity. International Centre for Mechanical Sciences, vol 299. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2618-9_1
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DOI: https://doi.org/10.1007/978-3-7091-2618-9_1
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82191-6
Online ISBN: 978-3-7091-2618-9
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