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Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling
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Convex Functions and Optimization Methods on Riemannian Manifolds (Paperback, Softcover reprint of hardcover 1st ed. 1994)
Loot Price: R4,484
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Convex Functions and Optimization Methods on Riemannian Manifolds (Paperback, Softcover reprint of hardcover 1st ed. 1994)
Series: Mathematics and Its Applications, 297
Expected to ship within 10 - 15 working days
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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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