Optimal Processes on Manifolds
Author: R Nottrot
Publisher: Springer
Published: 2014-01-15
Total Pages: 136
ISBN-13: 9783662169704
DOWNLOAD EBOOKRead and Download eBook Full
Author: R Nottrot
Publisher: Springer
Published: 2014-01-15
Total Pages: 136
ISBN-13: 9783662169704
DOWNLOAD EBOOKAuthor: R. Nottrot
Publisher: Springer
Published: 2006-11-15
Total Pages: 131
ISBN-13: 3540395512
DOWNLOAD EBOOKAuthor: Roelof Nottrot
Publisher: Springer
Published: 1982-01-01
Total Pages: 124
ISBN-13: 9780387119632
DOWNLOAD EBOOKAuthor: Roelof Nottrot
Publisher:
Published: 1982
Total Pages: 0
ISBN-13: 9780387119632
DOWNLOAD EBOOKAuthor: Feng-yu Wang
Publisher: World Scientific
Published: 2013-09-23
Total Pages: 392
ISBN-13: 9814452661
DOWNLOAD EBOOKStochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.
Author: L.S. Pontryagin
Publisher: CRC Press
Published: 1987-03-06
Total Pages: 392
ISBN-13: 9782881240775
DOWNLOAD EBOOKThe fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.
Author: Lev Semenovich Pontri͡agin
Publisher:
Published: 1962
Total Pages: 384
ISBN-13:
DOWNLOAD EBOOKAuthor: C. Udriste
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 365
ISBN-13: 9401583900
DOWNLOAD EBOOKThe 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.
Author: Lawrence Conlon
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 402
ISBN-13: 1475722842
DOWNLOAD EBOOKThis book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.
Author: Robert Simon Fong
Publisher: Springer Nature
Published: 2022-05-17
Total Pages: 171
ISBN-13: 303104293X
DOWNLOAD EBOOKManifold optimization is an emerging field of contemporary optimization that constructs efficient and robust algorithms by exploiting the specific geometrical structure of the search space. In our case the search space takes the form of a manifold. Manifold optimization methods mainly focus on adapting existing optimization methods from the usual “easy-to-deal-with” Euclidean search spaces to manifolds whose local geometry can be defined e.g. by a Riemannian structure. In this way the form of the adapted algorithms can stay unchanged. However, to accommodate the adaptation process, assumptions on the search space manifold often have to be made. In addition, the computations and estimations are confined by the local geometry. This book presents a framework for population-based optimization on Riemannian manifolds that overcomes both the constraints of locality and additional assumptions. Multi-modal, black-box manifold optimization problems on Riemannian manifolds can be tackled using zero-order stochastic optimization methods from a geometrical perspective, utilizing both the statistical geometry of the decision space and Riemannian geometry of the search space. This monograph presents in a self-contained manner both theoretical and empirical aspects of stochastic population-based optimization on abstract Riemannian manifolds.