Robust Accelerated Gradient Methods for Smooth Strongly Convex Functions
نویسندگان
چکیده
منابع مشابه
A Robust Accelerated Optimization Algorithm for Strongly Convex Functions
This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient noise versus worst-case convergence rate. At one extreme, the algorithm is faster than Nesterov’s Fast Gradient Method by a constant factor but more fragile to...
متن کاملOptimization of Smooth and Strongly Convex Functions
A. Proof of Lemma 1 We need the following lemma that characterizes the property of the extra-gradient descent. Lemma 8 (Lemma 3.1 in (Nemirovski, 2005)). Let Z be a convex compact set in Euclidean space E with inner product 〈·, ·〉, let ‖ · ‖ be a norm on E and ‖ · ‖∗ be its dual norm, and let ω(z) : Z 7→ R be a α-strongly convex function with respect to ‖ · ‖. The Bregman distance associated wi...
متن کاملIntermediate Gradient Methods for Smooth Convex Problems with Inexact Oracle
Between the robust but slow (primal or dual) gradient methods and the fast but sensitive to errors fast gradient methods, our goal in this paper is to develop first-order methods for smooth convex problems with intermediate speed and intermediate sensitivity to errors. We develop a general family of first-order methods, the Intermediate Gradient Method (IGM), based on two sequences of coefficie...
متن کاملAccelerated gradient sliding for structured convex optimization
Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding (AGS) method for minimizing the summation of two smooth convex functions with different Lipschitz constants. We show that the AGS method can skip the gradient...
متن کاملOn the quadratic support of strongly convex functions
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
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: SIAM Journal on Optimization
سال: 2020
ISSN: 1052-6234,1095-7189
DOI: 10.1137/19m1244925