A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method
نویسندگان
چکیده
منابع مشابه
Steepest descent method on a Riemannian manifold: the convex case
In this paper we are interested in the asymptotic behavior of the trajectories of the famous steepest descent evolution equation on Riemannian manifolds. It writes ẋ (t) + gradφ (x (t)) = 0. It is shown how the convexity of the objective function φ helps in establishing the convergence as time goes to infinity of the trajectories towards points that minimize φ. Some numerical illustrations are ...
متن کاملA hybrid steepest descent method for constrained convex optimization
This paper describes a hybrid steepest descent method to decrease over time any given convex cost function while keeping the optimization variables into any given convex set. The method takes advantage of properties of hybrid systems to avoid the computation of projections or of a dual optimum. The convergence to a global optimum is analyzed using Lyapunov stability arguments. A discretized imp...
متن کاملSoliton approach to the noisy Burgers equation Steepest descent method
The noisy Burgers equation in one spatial dimension is analyzed by means of the Martin-SiggiaRose technique in functional form. In a canonical formulation the morphology and scaling behavior are accessed by mean of a principle of least action in the asymptotic non-perturbative weak noise limit. The ensuing coupled saddle point field equations for the local slope and noise fields, replacing the ...
متن کاملSteepest descent method for quasiconvex minimization on Riemannian manifolds
This paper extends the full convergence of the steepest descent algorithm with a generalized Armijo search and a proximal regularization to solve quasiconvex minimization problems defined on complete Riemannian manifolds. Previous convergence results are obtained as particular cases of our approach and some examples in non Euclidian spaces are given.
متن کاملGeometric Descent Method for Convex Composite Minimization
In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh [5] to solving nonsmooth and strongly convex composite problems. We prove that the resulting algorithm, GeoPG, converges with a linear rate (1− 1/√κ), thus achieves the optimal rate among first-order methods, where κ is the condition number of the problem. Numerical results on linear regression and ...
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 Differential Equations
سال: 1996
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.0104