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Titlebook: Convex Functions and Optimization Methods on Riemannian Manifolds; Constantin Udrişte Book 1994 Springer Science+Business Media Dordrecht

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发表于 2025-3-21 16:49:12 | 显示全部楼层 |阅读模式
书目名称Convex Functions and Optimization Methods on Riemannian Manifolds
编辑Constantin Udrişte
视频video
丛书名称Mathematics and Its Applications
图书封面Titlebook: Convex Functions and Optimization Methods on Riemannian Manifolds;  Constantin Udrişte Book 1994 Springer Science+Business Media Dordrecht
描述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 fun
出版日期Book 1994
关键词Convexity; Mathematica; Riemannian geometry; algorithm; algorithms; differential equation; dynamical syste
版次1
doihttps://doi.org/10.1007/978-94-015-8390-9
isbn_softcover978-90-481-4440-2
isbn_ebook978-94-015-8390-9
copyrightSpringer Science+Business Media Dordrecht 1994
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发表于 2025-3-21 23:28:25 | 显示全部楼层
https://doi.org/10.34157/978-3-648-16940-7 As a matter of fact, the Euclidean conjugate direction method is nothing else than a descent method on a particular Riemannian space (ℝ. and a metric with constant components, i.e. , an Euclidean space) . One should also have in mind the approximations of the extrema of energies of the vector fields .
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Book 1994programs 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 manifold
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https://doi.org/10.34157/978-3-648-16940-7in in the tangent space (Euclidean) T.M. This fact suggested the idea that usual numerical methods for optimization on Euclidean spaces would be also sufficient as numerical methods on Riemannian manifolds. Our investigations, started in 1976, pointed out the failure of this point of view and the ne
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https://doi.org/10.34157/978-3-648-16916-2The main purpose of this section lies in the study of the Hessian of the p-energy of a curve at each critical point and in the geometrical interpretation of Jacobi fields.
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