Optimal Quadratic and Qcqp Algorithms With Applications: 23 - Rilegato

Dostl, Zdenek

Rilegato

ISBN 10: 3031951662 ISBN 13: 9783031951664

Casa editrice: Springer Nature, 2025

Riassunto

This book presents cutting-edge algorithms for solving large-scale quadratic programming (QP) and/or by the Hessian's spectrum. While applying these algorithms to the class of QP problems with the spectrum confined to a positive interval, the theory guarantees finding the prescribed precision solution through a uniformly bounded number of simple iterations, like matrix-vector multiplications.

Key concepts explored include the active set strategy, spectral gradients, and augmented Lagrangian methods. The book provides a comprehensive quantitative convergence theory, avoiding unspecified constants. Through detailed numerical experiments, the author demonstrates the algorithms' superior performance compared to traditional methods, especially in handling large problems with sparse Hessian. The performance of the algorithms is shown on large-scale (billions of variables) problems of mechanics, optimal control, and support vector machines.

Ideal for researchers and practitioners in optimization and computational mathematics, this volume is also an introductory text and a reference for advanced studies in nonlinear programming. Whether you're a scholar in applied mathematics or an engineer tackling complex optimization challenges, this book offers valuable insights and practical tools for your work.

Su questo libro

Informazioni sull?autore

Zdenek Dostįl is a professor at the Department of Applied Mathematics and Senior Researcher at IT4Innovations National Supercomputing Center, VŠB-Technical University of Ostrava. Zdenek works in Numerical Linear Algebra, Optimization, and Computational Mechanics. He published his results in more than 120 papers (Scopus). He is an author of the book ‘Optimal Quadratic Programming Algorithms’ (Springer 2009) and coauthor of ‘Scalable Algorithms for Contact Problems’ (Springer 2017) on massively parallel algorithms with theoretically supported linear (optimal) complexity. His current research concerns QP, QCQP, and generalization of the above results to H-TFETI and H-TBETI.

Dalla quarta di copertina

This book presents cutting-edge algorithms for solving large-scale quadratic programming (QP) and/or QCQP (quadratic constraint) problems, with the convergence rate determined by the Hessian's spectrum. While applying these algorithms to the class of QP problems with the spectrum confined to a positive interval, the theory guarantees finding the prescribed precision solution through a uniformly bounded number of simple iterations, like matrix-vector multiplications.

Key concepts explored include the active set strategy, spectral gradients, and augmented Lagrangian methods. This book provides a comprehensive quantitative convergence theory, avoiding unspecified constants. Through detailed numerical experiments, the author demonstrates the algorithms' superior performance compared to traditional methods, especially in handling large problems with sparse Hessian. The performance of the algorithms is shown on large-scale (billions of variables) problems of mechanics, optimal control, and support vector machines.

Ideal for researchers and practitioners in optimization and computational mathematics, this volume is also an introductory text and a reference for advanced studies in nonlinear programming. Whether you're a scholar in applied mathematics or an engineer tackling complex optimization challenges, this book offers valuable insights and practical tools for your work.

Dettagli dell'edizione

• Editore: Springer Nature
• Data di pubblicazione: 2025
• Lingua: Inglese
• ISBN 10: 3031951662
• ISBN 13: 9783031951664
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 399
• Contatto del produttore: Elevation; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; 22391; Germania