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Numerical optimization and quasiconvexity

Published online by Cambridge University Press:  26 September 2008

P. A. Gremaud
P. A. Gremaud
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

In the Calculus of Variations, several notions of convexity have emerged, corresponding to different properties of the functionals to be minimized. The relations between these various notions are not yet fully understood. In this context, we present a numerical study of quasiconvexity for some functions of the type f(ξ) = g(|ξ|2, det ξ), where Ξ is a 2×2-matrix. The corresponding global optimization problems are solved using a simulated annealing-like algorithm. The computations strongly indicate that the considered functions are quasiconvex if and only if they are rank-one convex. The relation to Morrey's conjecture, various applications and implementation problems are discussed.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 1 , February 1995 , pp. 69 - 82
Copyright
Copyright © Cambridge University Press 1995

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