Projected Hessian Updating Algorithms for Nonlinearly Constrained Optimization

Jorge Nocedal, Michael Overton

ISBN 10: 1334213712 / ISBN 13: 9781334213717

Editore: Forgotten Books, 2024

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Print on Demand. This book delves into the topic of solving nonlinearly constrained optimization problems, a complex mathematical challenge with wide-ranging applications in engineering, economics, and other fields. The author, an expert in optimization methods, presents a comprehensive analysis of projected Hessian updating algorithms, a specialized technique for solving these problems efficiently. The heart of the book lies in the detailed examination of the theoretical properties of projected Hessian updating algorithms. The author meticulously proves their convergence properties, ensuring that they can reliably find solutions to nonlinearly constrained optimization problems. Furthermore, the book provides valuable insights into the strengths and limitations of different variants of these algorithms. This knowledge equips readers with the tools to select the most appropriate algorithm for their specific problem. Overall, this book offers a deep understanding of projected Hessian updating algorithms, positioning them within the broader context of nonlinear optimization. Its rigorous analysis and practical guidance make it an essential resource for researchers, practitioners, and anyone seeking to master this advanced optimization technique. 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 9781334213717_0

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Titolo: Projected Hessian Updating Algorithms 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 Projected Hessian Updating Algorithms for Nonlinearly Constrained Optimization

Hessian, a symmetric matrix of order n - m.which can be expected to be_3_ positive definite near a solution This idea was suggested by Murray and Wright (1978) and has also been discussed by several other authors. We present several variants of this algorithm and prove that under certain conditions they all have a local two-step O - superlinear convergence property. Finally, in Section 5 we present some numerical results which indicate that these methods may be very useful in practice.

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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.