subgradient methodshuge-scale problemssublinear iteration costIn this paper, we develop a primal-dual subgradient method for solving huge-scale linear conic optimization problems. Our main assumption is that the primal cone is formed as a direct product of many small-dimensional convex cones and that...
Primal-dual subgradient methods for minimizing uniformly convex functions - Juditsky, Nesterov - 2010 () Citation Context ...ns are not necessarily strongly convex. If µ > 0 in (1.2), then, by the classic complexity theory for convex programming (see, e.g., Theorems 5.3.1 and 7.2.6 ...
Nesterov, Y.: Primal-dual subgradient methods for convex problems. Math. Programm. 120(1), 221–259 (2009) Article MathSciNet Google Scholar Shalev-Shwartz, S., Ben-David, S.: Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, Cambridge (2014) Book Google...
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2008/60 ■ barrier subgradient method barrier subgradient method We propose two approximate versions of the first-order primaldual algorithm (PDA) to solve a class of convex-concave saddle point problems. The introduced ... N Yu 被引量: 0发表: 2017年 加载更多来源...
Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on ...
The next important advancement in this area is related to development of themirror descent method(MDM) ( [2], see also [1]). In this scheme, the main information is accumulated in the dual space in the form of aggregated subgradients. For defining the next test point, this object is ma...
[13], [14], [15], [16], [17], [18], [19], among which the distributed subgradient or gradient algorithms [7], [8], [9], [10], [11] belong to the primal domain methods while [12], [13], [14], [15], [16], [17], [18], [19] belong to the primal–dual domain ...
We study the convergence behaviors of primal–dual hybrid gradient (PDHG) for solving linear programming (LP). PDHG is the base algorithm of a new general-purpose first-order method LP solver, PDLP, which aims to scale up LP by taking advantage of modern computing architectures. Despite its ...
We prove that if the coupling matrix $A$ has full column rank, the vanilla primal-dual gradient method can achieve linear convergence even if $f$ is not strongly convex. Our result generalizes previous work which either requires $f$ and $g$ to be quadratic functions or requires proximal ...