{"title":"Minimum volume ellipsoids - theory and algorithms","authors":"M. Todd","doi":"10.1137/1.9781611974386","DOIUrl":"https://doi.org/10.1137/1.9781611974386","url":null,"abstract":"","PeriodicalId":215971,"journal":{"name":"MOS-SIAM Series on Optimization","volume":"56 1-2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133006442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Electrical transmission system cascades and vulnerability - an operations research viewpoint","authors":"D. Bienstock","doi":"10.1137/1.9781611974164","DOIUrl":"https://doi.org/10.1137/1.9781611974164","url":null,"abstract":"The power grid can be considered one of twentieth-century engineering s greatest achievements, and as grids and populations grow, robustness is a factor that planners must take into account. Power grid robustness is a complex problem for two reasons: the underlying physics is mathematically complex, and modeling is complicated by lack of accurate data. This book sheds light on this complex problem by introducing the engineering details of power grid operations from the basic to the detailed; describing how to use optimization and stochastic modeling, with special focus on the modeling of cascading failures and robustness; providing numerical examples that show \"how things work\"; and detailing the application of a number of optimization theories to power grids. Audience: This book is intended for operations researchers who want to learn about power grids and power engineers who seek a more in-depth understanding of optimization methodologies and of the rigorous thinking used in optimization.","PeriodicalId":215971,"journal":{"name":"MOS-SIAM Series on Optimization","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127654752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Evaluating Gas Network Capacities","authors":"T. Koch, Benjamin Hiller, M. Pfetsch, L. Schewe","doi":"10.1137/1.9781611973693","DOIUrl":"https://doi.org/10.1137/1.9781611973693","url":null,"abstract":"This book addresses a seemingly simple question: Can a certain amount of gas be transported within a pipeline network? The question is difficult, however, when asked in relation to a meshed nationwide gas transportation network and when taking into account technical details and discrete decisions, as well as regulations, contracts, and varying demands involved. Evaluating Gas Network Capacities provides an introduction to the field of gas transportation planning and discusses in detail the advantages and disadvantages of several mathematical models that address gas transport within the context of the technical and regulatory framework. It shows how to solve the models using sophisticated mathematical optimization algorithms and includes examples of large-scale applications of mathematical optimization to this real-world industrial problem. Readers will also find a glossary of gas transport terms, tables listing the physical and technical quantities and constants used throughout the book, and a reference list of regulation and gas business literature. Audience: This book is intended for mathematicians interested in industrial applications. Engineers working in gas transport will also find the book of interest.","PeriodicalId":215971,"journal":{"name":"MOS-SIAM Series on Optimization","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129613442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebraic and Geometric Ideas in the Theory of Discrete Optimization","authors":"J. D. Loera, R. Hemmecke, M. Köppe","doi":"10.1137/1.9781611972443","DOIUrl":"https://doi.org/10.1137/1.9781611972443","url":null,"abstract":"This book presents recent advances in the mathematical theory of discrete optimization, particularly those supported by methods from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside the standard curriculum in optimization. Algebraic and Geometric Ideas in the Theory of Discrete Optimization offers several research technologies not yet well known among practitioners of discrete optimization, minimizes prerequisites for learning these methods, and provides a transition from linear discrete optimization to nonlinear discrete optimization. Audience: This book can be used as a textbook for advanced undergraduates or beginning graduate students in mathematics, computer science, or operations research or as a tutorial for mathematicians, engineers, and scientists engaged in computation who wish to delve more deeply into how and why algorithms do or do not work. Contents: Part I: Established Tools of Discrete Optimization; Chapter 1: Tools from Linear and Convex Optimization; Chapter 2: Tools from the Geometry of Numbers and Integer Optimization; Part II: Graver Basis Methods; Chapter 3: Graver Bases; Chapter 4: Graver Bases for Block-Structured Integer Programs; Part III: Generating Function Methods; Chapter 5: Introduction to Generating Functions; Chapter 6: Decompositions of Indicator Functions of Polyhedral; Chapter 7: Barvinok s Short Rational Generating Functions; Chapter 8: Global Mixed-Integer Polynomial Optimization via Summation; Chapter 9: Multicriteria Integer Linear Optimization via Integer Projection; Part IV: Grbner Basis Methods; Chapter 10: Computations with Polynomials; Chapter 11: Grbner Bases in Integer Programming; Part V: Nullstellensatz and Positivstellensatz Relaxations; Chapter 12: The Nullstellensatz in Discrete Optimization; Chapter 13: Positivity of Polynomials and Global Optimization; Chapter 14: Epilogue.","PeriodicalId":215971,"journal":{"name":"MOS-SIAM Series on Optimization","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126632714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introduction to Optimization and Semidifferential Calculus","authors":"M. Delfour","doi":"10.1137/1.9781611972153","DOIUrl":"https://doi.org/10.1137/1.9781611972153","url":null,"abstract":"1. Introduction 2. Existence, convexities, and convexification 3. Semi-differentiability, differentiability, continuity, and convexities 4. Optimality conditions 5. Constrained differentiable optimization Appendix A. Inverse and implicit function theorems Appendix B. Answers to exercises.","PeriodicalId":215971,"journal":{"name":"MOS-SIAM Series on Optimization","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128104531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces","authors":"M. Ulbrich","doi":"10.1137/1.9781611970692","DOIUrl":"https://doi.org/10.1137/1.9781611970692","url":null,"abstract":"Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including optimal control of semilinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods. Audience: This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization, and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities. It is also suitable as a text for an advanced graduate-level course in the aforementioned topics or applied functional analysis. Contents: Notation; Preface; Chapter One: Introduction; Chapter Two: Elements of Finite-Dimensional Nonsmooth Analysis; Chapter Three: Newton Methods for Semismooth Operator Equations; Chapter Four: Smoothing Steps and Regularity Conditions; Chapter Five: Variational Inequalities and Mixed Problems; Chapter Six: Mesh Independence; Chapter Seven: Trust-Region Globalization; Chapter Eight: State-Constrained and Related Problems; Chapter Nine: Several Applications; Chapter Ten: Optimal Control of Incompressible Navier-Stokes Flow; Chapter Eleven: Optimal Control of Compressible Navier-Stokes Flow; Appendix; Bibliography; Index.","PeriodicalId":215971,"journal":{"name":"MOS-SIAM Series on Optimization","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132288739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Trust Region Methods","authors":"A. Conn, N. Gould, P. Toint","doi":"10.1137/1.9780898719857","DOIUrl":"https://doi.org/10.1137/1.9780898719857","url":null,"abstract":"Preface 1. Introduction Part I. Preliminaries: 2. Basic Concepts 3. Basic Analysis and Optimality Conditions 4. Basic Linear Algebra 5. Krylov Subspace Methods Part II. Trust-Region Methods for Unconstrained Optimization: 6. Global Convergence of the Basic Algorithm 7.The Trust-Region Subproblem 8. Further Convergence Theory Issues 9. Conditional Models 10. Algorithmic Extensions 11. Nonsmooth Problems Part III. Trust-Region Methods for Constrained Optimization with Convex Constraints: 12. Projection Methods for Convex Constraints 13. Barrier Methods for Inequality Constraints Part IV. Trust-Region Mewthods for General Constained Optimization and Systems of Nonlinear Equations: 14. Penalty-Function Methods 15. Sequential Quadratic Programming Methods 16. Nonlinear Equations and Nonlinear Fitting Part V. Final Considerations: Practicalities Afterword Appendix: A Summary of Assumptions Annotated Bibliography Subject and Notation Index Author Index.","PeriodicalId":215971,"journal":{"name":"MOS-SIAM Series on Optimization","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126294696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
