{"title":"Boris S Mordukhovich","description":null,"products":[{"product_id":"second-order-variational-analysis-in-optimization-variational-stability-and-cont-book-boris-s-mordukhovich-9783031534751","title":"Second-Order Variational Analysis in Optimization, Variational Stability, and Control","description":"This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundlehren volumes Variational Analysis and Generalized Differentiation: I Basic Theory, II Applications (2006). This present book is the first entirely devoted to second-order variational analysis with numerical algorithms and applications to practical models. It covers a wide range of topics including theoretical, numerical, and implementations that will interest researchers in analysis, applied mathematics, mathematical economics, engineering, and optimization. Inclusion of a variety of exercises and commentaries in each chapter allows the book to be used effectively in a course on this subject. This area has been well recognized as an important and rapidly developing area of nonlinear analysis and optimization with numerous applications. Consisting of 9 interrelated chapters, the book is self-contained with the inclusion of some preliminaries in Chapter 1. Results presented are useful tools for characterizations of fundamental notions of variational stability of solutions for diverse classes of problems in optimization and optimal control, the study of variational convexity of extended-real-valued functions and their specifications and variational sufficiency in optimization.  Explicit calculations and important applications of second-order subdifferentials associated with the achieved characterizations of variational stability and related concepts, to the design and justification of second-order numerical algorithms for solving various classes of optimization problems, nonsmooth equations, and subgradient systems, are included. Generalized Newtonian algorithms are presented that show local and global convergence with linear, superlinear, and quadratic convergence rates. Algorithms are implemented to address interesting practical problems from the fields of machine learning, statistics, imaging, and other areas.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51063126098193,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51063128883473,"sku":"NIN9783031534751","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52608612860177,"sku":"NLS9783031534751","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3031534751.jpg?v=1750773397"},{"product_id":"variational-analysis-and-generalized-differentiation-i-book-boris-s-mordukhovich-9783540254379","title":"Variational Analysis and Generalized Differentiation I","description":"Variational analysis is an area in mathematics that, on the one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. This covers the theory of variational analysis.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52151006429457,"sku":"NLS9783540254379","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540254379.jpg?v=1757611888"},{"product_id":"variational-analysis-and-generalized-differentiation-ii-book-boris-s-mordukhovich-9783540254386","title":"Variational Analysis and Generalized Differentiation II","description":"Variational analysis is an area in mathematics that deals with the study of optimization and equilibrium problems and also applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. This book describes various applications of variational analysis.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52151012426001,"sku":"NLS9783540254386","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540254386.jpg?v=1757611907"},{"product_id":"variational-analysis-and-generalized-differentiation-i-book-boris-s-mordukhovich-9783642064821","title":"Variational Analysis and Generalized Differentiation I","description":"Variational analysis is a fruitful area in mathematics that, on one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature.    This monograph in 2 volumes contains a comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces and presents numerous applications to problems in optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first volume is devoted to the basic theory of variational analysis and generalized differentiations, while the second volume describes various applications. Both volumes include abundant bibliographies and extensive commentaries.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52332735562001,"sku":"NLS9783642064821","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642064821.jpg?v=1758152541"},{"product_id":"variational-analysis-and-generalized-differentiation-ii-book-boris-s-mordukhovich-9783642064838","title":"Variational Analysis and Generalized Differentiation II","description":"This monograph in two volumes contains a comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces and presents numerous applications to problems in optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first volume is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume describes various applications. Both volumes include abundant bibliographies and extensive commentaries.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52332745687313,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52332746506513,"sku":"NLS9783642064838","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642064838.jpg?v=1758152574"},{"product_id":"variational-analysis-and-applications-book-boris-s-mordukhovich-9783319927732","title":"Variational Analysis and Applications","description":"Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52507936227601,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52507936751889,"sku":"NLS9783319927732","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319927732.jpg?v=1760351435"},{"product_id":"nonsmooth-analysis-and-geometric-methods-in-deterministic-optimal-control-book-boris-s-mordukhovich-9781461384915","title":"Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control","description":"This IMA Volume in Mathematics and its Applications NONSMOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on Control Theory.  The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de- veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program- ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz- ing the workshop and editing the proceedings. We also take this oppor- tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52617565929745,"sku":"NLS9781461384915","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461384915.jpg?v=1761530688"},{"product_id":"variational-analysis-and-applications-book-boris-s-mordukhovich-9783030065133","title":"Variational Analysis and Applications","description":"Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research.    The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters\/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52618529669393,"sku":"NLS9783030065133","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030065133.jpg?v=1761533387"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-boris-s-mordukhovich.oembed","provider":"World of Books ","version":"1.0","type":"link"}