On a Saddle-Point Theorem in Minimum Compliance Design
J. J. Telega , Tomasz Lewiński
AbstractThis 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.
|Journal series||Journal of Optimization Theory and Applications, ISSN 0022-3239|
|Publication size in sheets||0.5|
|Keywords in English||Applications of Mathematics, Calculus of Variations and Optimal Control, duality, Engineering, general, minimization of compliance, Operation Research/Decision Theory, optimization, saddle points, Theory of Computation|
|ASJC Classification||; ;|
|Publication indicators||= 2; = 1; = 4.0; : 2000 = 1.041; : 2006 = 0.633 (2) - 2007=1.063 (5)|
|Citation count*||5 (2020-09-08)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.