Tag: Convex

Free Download Convex Stochastic Optimization: Dynamic Programming and Duality in Discrete Time
English | 2024 | ISBN: 3031764315 | 423 Pages | PDF EPUB (True) | 36 MB
This book studies a general class of convex stochastic optimization (CSO) problems that unifies many common problem formulations from operations research, financial mathematics and stochastic optimal control. We extend the theory of dynamic programming and convex duality to allow for a unified and simplified treatment of various special problem classes found in the literature. The extensions allow also for significant generalizations to existing problem formulations. Both dynamic programming and duality have played crucial roles in the development of various optimality conditions and numerical techniques for the solution of convex stochastic optimization problems.

Free Download Strange Phenomena in Convex and Discrete Geometry By Chuanming Zong (auth.), James J. Dudziak (eds.)
1996 | 158 Pages | ISBN: 0387947345 | PDF | 4 MB
Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult – such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) – in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

Free Download C. Udriste, "Convex Functions and Optimization Methods on Riemannian Manifolds"
English | 1994 | pages: 367 | ISBN: 904814440X, 0792330021 | DJVU | 2,3 mb
The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers. It contains mathematical information on these subjects and applications distributed in seven chapters whose topics are close to my own areas of research: Metric properties of Riemannian manifolds, First and second variations of the p-energy of a curve; Convex functions on Riemannian manifolds; Geometric examples of convex functions; Flows, convexity and energies; Semidefinite Hessians and applications; Minimization of functions on Riemannian manifolds. All the numerical algorithms, computer programs and the appendices (Riemannian convexity of functions f:R ~ R, Descent methods on the Poincare plane, Descent methods on the sphere, Completeness and convexity on Finsler manifolds) constitute an attempt to make accesible to all users of this book some basic computational techniques and implementation of geometric structures. To further aid the readers,this book also contains a part of the folklore about Riemannian geometry, convex functions and dynamical systems because it is unfortunately "nowhere" to be found in the same context; existing textbooks on convex functions on Euclidean spaces or on dynamical systems do not mention what happens in Riemannian geometry, while the papers dealing with Riemannian manifolds usually avoid discussing elementary facts. Usually a convex function on a Riemannian manifold is a real valued function whose restriction to every geodesic arc is convex.

Free Download A Course in Robust Control Theory: A Convex Approach by Geir E. Dullerud , Fernando Paganini
English | PDF | 2000 | 427 Pages | ISBN : 0387989455 | 34.9 MB
Research in robust control theory has been one of the most active areas of mainstream systems theory since the late 70s. This research activity has been at the confluence of dynamical systems theory, functional analysis, matrix analysis, numerical methods, complexity theory, and engineering applications. The discipline has involved interactions between diverse research groups including pure mathematicians, applied mathematicians, computer scientists and engineers. This research effort has produced a rather extensive set of approaches using a wide variety of mathematical techniques, and applications of robust control theory are spreading to areas as diverse as control of fluids, power networks, and the investigation of feddback mechanisms in biology. During the 90’s the theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on robust control theory that emphasizes these new developments, but at the same time conveys the main principles and ubiquitous tools at the heart of the subject. Its pedagogical objectives are to introduce a coherent and unified framework for studying robust control theory, to provide students with the control-theoretic background required to read and contribute to the research literature, and to present the main ideas and demonstrations of the major results of robust control theory. The book will be of value to mathematical researchers and computer scientists wishing to learn about robust control theory, graduate students planning to do research in the area, and engineering practitioners requiring advanced control techniques.

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.