Accelerated dual-averaging primal–dual method for composite convex minimization
نویسندگان
چکیده
منابع مشابه
Geometric 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 کاملDoubly Accelerated Stochastic Variance Reduced Dual Averaging Method for Regularized Empirical Risk Minimization
In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the machine learning community, because mini-batch settings stabilize the gradient estimate and can easily make good use of parallel computing. The core of our pr...
متن کاملSupplementary Material: Geometric Descent Method for Convex Composite Minimization
We argue that the geometric intuition of GeoPG is still clear. Note that we are still constructing two balls that contain x∗ and shrink at the same absolute amount. In GeoPG, since we assume that the smooth function f is strongly convex, we naturally have one ball that contains x∗, and this ball is related to the proximal gradient Gt, instead of the gradient due to the presence of the nonsmooth...
متن کاملCanonical Primal-Dual Method for Solving Non-convex Minimization Problems
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. Numerical examples are illustrated. Comparing...
متن کاملStochastic Three-Composite Convex Minimization
We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computationally advantageous to process smooth term in the decomposition with its stochastic gradient estimate and the other two functions separately ...
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: Optimization Methods and Software
سال: 2020
ISSN: 1055-6788,1029-4937
DOI: 10.1080/10556788.2020.1713779