Tag: Convex

Free Download Partha Dasgupta, Karl-Göran Mäler, "The Economics of Non-Convex Ecosystems"
English | 2004 | pages: 191 | ISBN: 1402019459, 1402018649 | PDF | 3,5 mb
Economists all too often assume that ecosystem and population dynamics are subject to convex (even linear) processes. However, research by ecosystem and population ecologists has shown that the processes in question are very often non-convex. This has important implications for environmental and resource economics. Typically, a system under study or being managed would contain multiple basins of attraction. So the system would flip from one basin to another if a "threshold" (mathematically, a bifurcation) were crossed. Furthermore, the flip could be irreversible. But even if it were reversible, the system could well display hysteresis. The latter eventuality means that in order to entice the system to return to its original basin of attraction, a different and possibly costly path has to be traced. A mistake in management may then be a lot more costly than envisaged. An example would be a possible flip of the Gulf Stream owing to fresh water intrusion from melting glaciers during global warming.

Free Download Solutions Manual to Accompany Geometry of Convex Sets by I. E. Leonard, J. E. Lewis
English | April 25, 2016 | ISBN: 1119184185 | 128 pages | PDF | 6.55 Mb
A Solutions Manual to accompany Geometry of Convex SetsGeometry of Convex Setsbegins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets ofn-dimensional space. Many properties of convex sets can be discovered using just the linear structure. However, for more interesting results, it is necessary to introduce the notion of distance in order to discuss open sets, closed sets, bounded sets, and compact sets. The book illustrates the interplay between these linear and topological concepts, which makes the notion of convexity so interesting.

Free Download A. R. Rajwade, "Convex Polyhedra with Regularity Conditions and Hilbert’s Third Problem"
English | 2002 | ISBN: 8185931283 | DJVU | pages: 128 | 1.6 mb

Free Download Marco Segala, "A Convex Mirror: Schopenhauer’s Philosophy and the Sciences"
English | ISBN: 019759915X | 2024 | 384 pages | EPUB, PDF | 2 MB + 22 MB
Schopenhauer is most recognizable as "the philosopher of pessimism," the author of a system that teaches how art and morality can help human beings navigate life in "the worst of all possible worlds." This dominant image of Schopenhauer has cut off an important branch of his tree of philosophy: the metaphysics of nature and its dialogue with the sciences of the time.

Free Download Convex Geometry
English | 2023 | ISBN: 3031378822 | 304 Pages | PDF EPUB (True) | 25 MB
Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn-Minkowski theory currently represents the central part of convex geometry.

Free Download Fundamentals of Convex Analysis and Optimization: A Supremum Function Approach
English | 2023 | ISBN: 3031295501 | 444 Pages | PDF EPUB (True) | 45 MB
This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers.

Free Download Tristan Buckmaster, "Intermittent Convex Integration for the 3D Euler Equations: (AMS-217) "
English | ISBN: 0691249555 | 2023 | 256 pages | PDF | 5 MB
A new threshold for the existence of weak solutions to the incompressible Euler equations

Free Download Aram V. Arutyunov, "Convex and Set-Valued Analysis "
English | ISBN: 3110460289 | 2016 | 210 pages | EPUB | 4 MB
This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The second part covers some important parts of set-valued analysis. There the properties of the Hausdorff metric and various continuity concepts of set-valued maps are considered. The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions. Contents:PrefacePart I: Convex analysisConvex sets and their propertiesThe convex hull of a set. The interior of convex setsThe affine hull of sets. The relative interior of convex setsSeparation theorems for convex setsConvex functionsClosedness, boundedness, continuity, and Lipschitz property of convex functionsConjugate functionsSupport functionsDifferentiability of convex functions and the subdifferentialConvex conesA little more about convex cones in infinite-dimensional spacesA problem of linear programmingMore about convex sets and convex hullsPart II: Set-valued analysisIntroduction to the theory of topological and metric spacesThe Hausdorff metric and the distance between setsSome fine properties of the Hausdorff metricSet-valued maps. Upper semicontinuous and lower semicontinuous set-valued mapsA base of topology of the spaceHc(X)Measurable set-valued maps. Measurable selections and measurable choice theoremsThe superposition set-valued operatorThe Michael theorem and continuous selections. Lipschitz selections. Single-valued approximationsSpecial selections of set-valued mapsDifferential inclusionsFixed points and coincidences of maps in metric spacesStability of coincidence points and properties of covering mapsTopological degree and fixed points of set-valued maps in Banach spacesExistence results for differential inclusions via the fixed point methodNotationBibliographyIndex

Free Download An Easy Path to Convex Analysis and Applications
English | 2023 | ISBN: 3031264576 | 313 Pages | PDF EPUB (True) | 32 MB
This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.