On a Saddle-Point Theorem in Minimum Compliance Design

J. J. Telega and T. Lewinski
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J. J. Telega: Polish Academy of Sciences
T. Lewinski: Warsaw University of Technology

Journal of Optimization Theory and Applications, 2000, vol. 106, issue 2, No 12, 450 pages

Abstract: Abstract This note deals with the displacement-based relaxed formulation of the minimum compliance layout problem of the optimal distribution of two isotropic materials within a given three-dimensional domain. In 1994, Lipton (Ref. 1) proved that minimization over elasticity tensors can be interchanged with maximization over displacements. This proof was based on the theory of Young measures. The aim of this contribution is to provide a new and straightforward proof of the Lipton saddle-point theorem by using a duality technique, thus bypassing the Young measure theory.

Keywords: saddle points; minimization of compliance; duality (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1004667901231

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