Optimality Conditions and Duality Theory for Minimizing Sums of the Largest

Michael L. Overton, Robert S. Womersley

ISBN 10: 1334016062 / ISBN 13: 9781334016066

Editore: Forgotten Books, 2024

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Print on Demand. This book meticulously details the mathematical theory and differential properties of sums of eigenvalues of symmetric matrices, examining both their largest and smallest eigenvalues. By establishing max characterizations for these values, the author successfully formulates necessary conditions for local minimizers. Additionally, the book provides a detailed analysis of the generalized gradient of eigenvalue sums, demonstrating the deep interconnections between the sets of positive semi-definite matrices and the sets of matrices whose eigenvalues lie within specific intervals. Through the development of model minimization algorithms, the book offers practical applications for the theoretical results presented, showcasing their significance in real-world problem-solving. The author's work expands our knowledge of eigenvalue sums and offers valuable insights for researchers in matrix theory and optimization. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. Codice articolo 9781334016066_0

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Titolo: Optimality Conditions and Duality Theory for...

Casa editrice: Forgotten Books

Data di pubblicazione: 2024

Legatura: Paperback

Condizione: New

Tipologia articolo: print-on-demand item

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Excerpt from Optimality Conditions and Duality Theory for Minimizing Sums of the Largest Eigenvalues of Symmetric Matrices

Note that the inequality U I is not required. Equation (1 11) is moderately well known; see Fletcher (1985) and Overton (1988.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.