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Rotationally Invariant Rank 1 Convex Functions

Rotationally Invariant Rank 1 Convex Functions . Let fbe a function on the set Mnxnof all nby nreal matrices. If fis rotationally invariant with respect to the proper orthogonal group, it has a representation \tilde f through the signed singular values of the matrix argument Å∈ M^nxn.Necessary and sufficient conditions are given for the rank 1 convexity of fin terms of \tilde f . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics & Optimization Springer Journals

Rotationally Invariant Rank 1 Convex Functions

Applied Mathematics & Optimization , Volume 44 (1) – Jan 1, 2001

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References (7)

Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag New York Inc. 2001
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-001-0012-z
Publisher site
See Article on Publisher Site

Abstract

. Let fbe a function on the set Mnxnof all nby nreal matrices. If fis rotationally invariant with respect to the proper orthogonal group, it has a representation \tilde f through the signed singular values of the matrix argument Å∈ M^nxn.Necessary and sufficient conditions are given for the rank 1 convexity of fin terms of \tilde f .

Journal

Applied Mathematics & OptimizationSpringer Journals

Published: Jan 1, 2001

Keywords: Key words. Rank 1 convex functions, Rotational invariance. AMS Classification. Primary 49K20, Secondary 73C50.

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