Convex Functions and Optimization Methods on Riemannian Manifolds

Name: Convex Functions and Optimization Methods on Riemannian Manifolds
Brand: Springer Netherlands
SKU: 9789048144402
Price: 649.23 PLN
Availability: InStock

Autor: Constantin Udriste

Język:

Oprawa: Miękka

Wydawca: Springer Netherlands

Dostępność: Dostępna u dostawcy

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The object of this book is to present the basic facts of convex functions, standard dynamical system...

Informacje o książce

Autor

Constantin Udriste

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2010

strony

350

EAN

9789048144402

ISBN

904814440X

Enbook ID

02715420

Wydawca

Springer Netherlands

Waga

569

Wymiary

160 x 240 x 19

Pełny opis

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.

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