Optimality Conditions and Duality Theory for Minimizing Sums of the Largest Eigenvalues of Symmetric Matrices (Classic Reprint) - Softcover

Michael L. Overton

 
9781334016066: Optimality Conditions and Duality Theory for Minimizing Sums of the Largest Eigenvalues of Symmetric Matrices (Classic Reprint)

Synopsis

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.

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