02760cam a2200361 i 4500 17984308 EG-ScBUE 20241021145102.0 131226t2014 sz a f b 001 0 eng d 9783319042466 CDX eng rda CDX YDXCP BTCTA UKMGB OCLCO MUU IUL DLC EG-ScBUE 22 515.64 IZM Izmailov, Alexey F., author. Newton-type methods for optimization and variational problems / Alexey F. Izmailov, Mikhail V. Solodov. Cham : Springer, [2014] c2014 xix, 573 pages : illustrations ; 24 cm. rdacontent text txt unmediated rdamedia n volume nc rdacarrier Springer series in operations research and financial engineering, 1431-8598 Includes bibliographical references and index. 1. Elements of optimization theory and variational analysis -- 2. Equations and unconstrained optimization -- 3. Variational problems: local methods -- 4. Constrained optimization: local methods -- 5. Variational problems: globalization of convergence -- 6. Constrained optimization: globalization of convergence -- 7. Degenerate problems with nonisolated solutions -- Appendix. This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.-- Calculus of variations. BUEsh 3105 Mathematical optimization. BUEsh 3485 Iterative methods (Mathematics) BUEsh 36944 BUEsh ENGELC October2016 Reading book Solodov, Mikhail V., author. ddc BB 22716 22688 0 0 ddc 0 0 Academic MAIN MAIN 1ST 2016-10-19 Purchase 1320.00 9155 0 515.64 IZM 000034335 2025-07-15 00:00:00 1650.00 2016-10-19 BB