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Numerical Computation of Rank-One Convex Envelopes

Dolzmann, Georg (1999) Numerical Computation of Rank-One Convex Envelopes. SIAM Journal on Numerical Analysis, 36 (5). pp. 1621-1635. ISSN 0036-1429. doi:10.1137/S0036142997325581.

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We describe an algorithm for the numerical computation of the rank-one convex envelope of a function $f:\MM^{m\times n}\rightarrow\RR$. We prove its convergence and an error estimate in L∞.

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Additional Information:© 1999 SIAM Received by the editors August 6, 1997; accepted for publication (in revised form) October 28, 1998; published electronically September 8, 1999. This work was partially supported by ARO and NSF through grants to the Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, PA. Most of the work was done while the author held a postdoctoral research fellowship at the Center for Nonlinear Analysis at Carnegie Mellon University, Pittsburgh, whose hospitality and stimulating atmosphere are gratefully acknowledged. It is my pleasure to thank N. J. Walkington for fruitful discussion on the subject. I also thank the referees for their insightful comments.
Subject Keywords:rank-one convexity; generalized convex envelopes; nonconvex variational problems
Issue or Number:5
Record Number:CaltechAUTHORS:DOLsiamjna99
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3090
Deposited By: Archive Administrator
Deposited On:15 May 2006
Last Modified:08 Nov 2021 19:53

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