Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds
نویسندگان
چکیده
منابع مشابه
Proximal Point Methods with Bregman Function on Riemannian Manifolds
We study the proximal point algorithm with Bregman type distance to minimize the problem , , . ) ( min S x to s x f ∈ where S is an open convex subset of a complete simply connected Riemannian manifold M of non positive sectional curvature and f is a convex function in this manifold. Introducing a strong assumption on the geodesic triangle on this manifold we obtain the convergence of the seque...
متن کاملε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds
This paper presents a descent direction method for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we define a set-valued mapping x → ∂εf(x) named ε-subdifferential which is an approximation for the Clarke subdifferential and which generalizes the Goldstein-ε-subdifferential to the Riemannian setting. Using this notion we construct a steepest descent ...
متن کاملAveraging Stochastic Gradient Descent on Riemannian Manifolds
We consider the minimization of a function defined on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradient descent (SGD) on M to an averaged iterate sequence with a robust and fast O(1/n) convergence rate. We then present an application of our...
متن کاملthe effect of task complexity on lexical complexity and grammatical accuracy of efl learners’ argumentative writing
بر اساس فرضیه شناخت رابینسون (2001 و 2003 و 2005) و مدل ظرفیت توجه محدود اسکهان (1998)، این تحقیق تاثیر پیچیدگی تکلیف را بر پیچیدگی واژگان و صحت گرامری نوشتار مباحثه ای 60 نفر از دانشجویان زبان انگلیسی بررسی کرد. میزان پیچیدگی تکلیف از طریق فاکتورهای پراکندگی-منابع تعیین شد. همه ی شرکت کنندگان به صورت نیمه تصادفی به یکی از سه گروه: (1) گروه موضوع، (2) گروه موضوع + اندیشه و (3) گروه موضوع + اندی...
15 صفحه اولProximal Point Method for a Class of Bregman Distances on Riemannian Manifolds
This paper generalizes the proximal point method using a class of Bregman distances to solve convex and quasiconvex optimization problems on complete Riemannian manifolds. We will prove, under standard assumptions, that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we give some examples of Bregman distances in non-Euclidean spaces.
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 Optimization Theory and Applications
سال: 2017
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-017-1093-4