Convex bodies : the Brunn-Minkowski theory / / Rolf Schneider, Albert-Ludwigs-Universitat Freiburg, Germany [[electronic resource]]

• Record Nr.: UNINA9910787619903321
• Autore: Schneider Rolf <1940->
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2014
• ISBN: 1-107-45500-6; 1-107-46205-3; 1-107-45983-4; 1-107-46906-6; 1-107-46552-4; 1-107-47267-9; 1-139-00385-2
• Edizione: [Second edition.]
• Descrizione fisica: 1 online resource (xxii, 736 pages) : digital, PDF file(s)
• Collana: Encyclopedia of mathematics and its applications ; ; volume 151
• Disciplina: 516.3/74
• Soggetti: Convex bodies
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: Basic convexity -- Boundary structure -- Minkowski addition -- Support measures and intrinsic volumes -- Mixed volumes and related concepts -- Valuations on convex bodies -- Inequalities for mixed volumes -- Determination by area measures and curvatures -- Extensions and analogues of the Brunn--Minkowski theory -- Affine constructions and inequalities.
• Sommario/riassunto: At the heart of this monograph is the Brunn-Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex ; bodies, on extensions like the Lp Brunn-Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.

Robust optimization [[electronic resource] /] / Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski

• Record Nr.: UNINA9910778219003321
• Autore: Ben-Tal A
• Pubbl/distr/stampa: Princeton, NJ, : Princeton University Press, c2009
• ISBN: 1-282-25928-8; 9786612259289; 1-4008-3105-9
• Edizione: [Course Book]
• Descrizione fisica: 1 online resource (565 p.)
• Collana: Princeton Series in Applied Mathematics ; ; 28
• Classificazione: SK 870
• Altri autori (Persone): El GhaouiLaurent; NemirovskiĭArkadiĭ Semenovich
• Disciplina: 519.6
• Soggetti: Robust optimization; Linear programming
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di contenuto: Frontmatter -- Contents -- Preface -- Part I. Robust Linear Optimization -- Chapter One. Uncertain Linear Optimization Problems and their Robust Counterparts -- Chapter Two. Robust Counterpart Approximations of Scalar Chance Constraints -- Chapter Three. Globalized Robust Counterparts of Uncertain LO Problems -- Chapter Four. More on Safe Tractable Approximations of Scalar Chance Constraints -- Part II. Robust Conic Optimization -- Chapter Five. Uncertain Conic Optimization: The Concepts -- Chapter Six. Uncertain Conic Quadratic Problems with Tractable RCs -- Chapter Seven. Approximating RCs of Uncertain Conic Quadratic Problems -- Chapter Eight. Uncertain Semidefinite Problems with Tractable RCs -- Chapter Nine. Approximating RCs of Uncertain Semidefinite Problems -- Chapter Ten. Approximating Chance Constrained CQIs and LMIs -- ; Chapter Eleven. Globalized Robust Counterparts of Uncertain Conic Problems -- Chapter Twelve. Robust Classi¯cation and Estimation -- Part III. Robust Multi-Stage Optimization -- Chapter Thirteen. Robust Markov Decision Processes -- Chapter Fourteen. Robust Adjustable Multistage Optimization -- Part IV. Selected Applications -- Chapter Fifteen. Selected Applications -- Appendix A: Notation and Prerequisites -- Appendix B: Some Auxiliary Proofs -- Appendix C: Solutions to Selected Exercises -- Bibliography -- Index
• Sommario/riassunto: Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.