Convexity and Optimization in Finite Dimensions I is popular PDF and ePub book, written by Josef Stoer in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Convexity and Optimization in Finite Dimensions I can be Read Online from any device for your convenience.
Convexity and Optimization in Finite Dimensions I Book PDF Summary
Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back ground for the arithmetic of convex optimization to be treated in a sub sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin's description of polyhedra, Minkowski's supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, respectively. The treatment of extremal properties of polyhedra as well as of general convex sets is based on the far reaching work of Klee. Chapter 2 terminates with a description of Gale diagrams, a recently developed successful technique for exploring polyhedral structures.
Detail Book of Convexity and Optimization in Finite Dimensions I PDF
- Author : Josef Stoer
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642462160
- Genre : Mathematics
- Total Page : 306 pages
- Language : English
- PDF File Size : 12,5 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Convexity and Optimization in Finite Dimensions I by Josef Stoer, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.