Convex functions and optimization methods on Riemannian manifolds
By: Constantin Udrişte.
Series: Mathematics and its applications ;; v. 297; Mathematics and its applications (Kluwer Academic Publishers) ;; v. 297.
Publisher: Kluwer Academic Publishers
Published: 1994
Place of publication: Dordrecht; Boston
Language: eng
Number of pages: 348
Subjects: Riemannian manifolds; Convex functions; Mathematical optimization
Description: This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems, and mathematical modelling. This book is the first account on the development of this subject as it emerged in the beginning of the 'seventies. Also, a unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is presented.

Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry.

An appendix is devoted to convexity and completeness in Finsler manifolds.
Notes: Includes bibliographical references (p. [331]-340) and index.