Third-order methods on Riemannian manifolds under Kantorovich conditions
نویسندگان
چکیده
منابع مشابه
Trust-Region Methods on Riemannian Manifolds
A general scheme for trust-region methods on Riemannian manifolds is proposed and analyzed. Among the various approaches available to (approximately) solve the trust-region subproblems, particular attention is paid to the truncated conjugate-gradient technique. The method is illustrated on problems from numerical linear algebra.
متن کاملIsoperimetric Conditions and Diffusions in Riemannian Manifolds
We study diiusions in Riemannian manifolds and properties of their exit time moments from smoothly bounded domains with compact closure. For any smoothly bounded domain with compact closure, ; and for each positive integer k; we characterize the kth exit time moment of Brownian motion, averaged over the domain with respect to the metric density, using a variational quotient. We prove that for R...
متن کاملHigher Order Jordan Osserman Pseudo-riemannian Manifolds
We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and nontrivial examples of higher order Osserman manifolds. Subject Classification: 53B20. PACS numbers: 0240, 0...
متن کاملCurvature Conditions on Riemannian Manifolds with Brownian Harmonicity Properties
The time and place that Brownian motion on a Riemannian manifold first exits a normal ball of radius e is considered and a general procedure is given for computing asymptotic expansions, as e decreases to zero, for joint moments of the first exit time and place random variables. It is proven that asymptotic versions of exit time and place distribution properties that hold on harmonic spaces are...
متن کاملOptimality conditions for the nonlinear programming problems on Riemannian manifolds
In recent years, many traditional optimization methods have been successfully generalized to minimize objective functions on manifolds. In this paper, we first extend the general traditional constrained optimization problem to a nonlinear programming problem built upon a general Riemannian manifold M , and discuss the first-order and the second-order optimality conditions. By exploiting the dif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2013.04.023