Hessian Riemannian Gradient Flows in Convex Programming

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hessian Riemannian Gradient Flows in Convex Programming

In view of solving theoretically constrained minimization problems, we investigate the properties of the gradient flows with respect to Hessian Riemannian metrics induced by Legendre functions. The first result characterizes Hessian Riemannian structures on convex sets as metrics that have a specific integration property with respect to variational inequalities, giving a new motivation for the ...

متن کامل

On Hessian Riemannian Structures

In Proposition 4.1 a characterization is given of Hessian Rieman-nian structures in terms of a natural connection in the general linear group GL(n; R) + , which is viewed as a principal SO(n)-bundle over the space of positive deenite symmetric n n-matrices. For n = 2, Proposition 5.3 contains an interpretation of the curvature of a Hessian Riemannian structure at a given point, in terms of an u...

متن کامل

Convergence to the optimal value for barrier methods combined with Hessian Riemannian gradient flows and generalized proximal algorithms

We consider the problem minx∈Rn{f(x) | Ax = b, x ∈ C, gj(x) ≤ 0, j = 1, . . . , s}, where b ∈ R, A ∈ R is a full rank matrix, C is the closure of a nonempty, open and convex subset C of R, and gj(·), j = 1, . . . , s, are nonlinear convex functions. Our strategy consists firstly in to introduce a barrier-type penalty for the constraints gj(x) ≤ 0, then endowing {x ∈ R | Ax = b, x ∈ C} with the ...

متن کامل

Numerical Integration of Riemannian Gradient Flows for Image Labeling

The image labeling problem can be described as assigning to each pixel a single element from a finite set of predefined labels. Recently, a smooth geometric approach was proposed [2] by following the Riemannian gradient flow of a given objective function on the socalled assignment manifold. In this paper, we adopt an approach from the literature on uncoupled replicator dynamics and extend it to...

متن کامل

Gradient Flows on a Riemannian Submanifold for Discrete Tomography

We present a smooth geometric approach to discrete tomography that jointly performs tomographic reconstruction and label assignment. The flow evolves on a submanifold equipped with a Hessian Riemannian metric and properly takes into account given projection constraints. The metric naturally extends the Fisher-Rao metric from labeling problems with directly observed data to the inverse problem o...

متن کامل

ذخیره 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: SIAM Journal on Control and Optimization

سال: 2004

ISSN: 0363-0129,1095-7138

DOI: 10.1137/s0363012902419977