First-order methods for convex and nonconvex optimization have been an important research topic in the past few years. This talk studies and develops efficient algorithms of first-order type, to solve a variety of problems. We first focus on the widely studied gradient-based methods in composite...
First-order methods are an important class of algorithms for convex and non-convex optimization. They are numerical schemes for minimizing the objective function, usually involving only the function value and its gradient or some approximation thereof at each iteration point. This is in contrast to ...
Devolder, O., Glineur, F., Nesterov, Y.: First order methods of smooth convex optimization with inexact oracle. Math. Program. Ser. A 146 (1–2), 37–75 (2014) MathSciNet MATHOlivier Devolder , Franois Glineur , Yurii Nesterov, First-order methods of smooth convex optimization with...
首先是first order methods在online learning中的自然应用,比如我们的问题改变定义,即我们在每个时间 t, 都有一个adversary选择一个 ft(⋅) 并report它在 xt 的(sub)gradient给我们。那么显然我们的算法可以直接用来进行"learning",我们的regret是 ∑t=1Tft(xt)−∑t=1Tft(x∗) (注意这里我们假设了目标 ...
a specialization to geodesically complete Riemannian manifolds: here, we devise and analyze the complexity of first-order methods for smooth minimax problems... P Zhang,J Zhang,S Sra - 《Siam Journal on Optimization A Publication of the Society for Industrial & Applied Mathematics》 被引量: 0发...
We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle (Math Program 145(1–2):451–482, 2014. doi:10.1007/s10107-013-0653-0) recently described a numerical method for computing the N-iteration optimal step coefficients in a class...
(but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well ...
methodslinearcomplementarityproblemsThe aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only consider bound constraints with (...
The primary goal of this book is to provide a self-contained, comprehensive study of the main first-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing ...
First-order Methods for Geodesically Convex Optimization Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-co... H Zhang,S Sra 被引量: 45发表: 2016年 Optimization of mechanical systems: On strate...