Distributed dual gradient methods and error bound conditions
By Ion Necoara, Valentin Nedelcu. 2014
15 citations recorded by the source corpus.
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal objective function we propose two distributed dual fast gradient schemes for which we prove sublinear rate of convergence for dual suboptimality but also primal suboptimality and feasibility violation for an average primal sequence or for the last generated primal iterate. Under the additional assumption of Lipshitz continuity of the gradient of the primal objective function we prove a global error bound type property for the dual problem and then we analyze a dual gradient scheme for which we derive global linear rate of convergence for both dual and primal suboptimality and primal feasibility violation. We also provide numerical simulations on optimal power flow problems.
Subfields: Artificial Intelligence, Computational Mechanics, Numerical Analysis
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Peter Richtárik
- Martin Jaggi
- Virginia Smith
- Jakub Konecný
- Martin Takác
- Chenxin Ma
- Michael I. Jordan
- Sebastian U. Stich
In Computational Mechanics
- Peter Richtárik
- Martin Takác
- Martin Jaggi
- Jakub Konecný
- Virginia Smith
- Chenxin Ma
- Michael I. Jordan
- Simone Forte
In Numerical Analysis
- Martin Takác
- Martin Jaggi
- Chenxin Ma
- Virginia Smith
- Michael I. Jordan
- Rachael Tappenden
- Simone Forte
- Francis R. Bach
Citations in the corpus
- CoCoA: A General Framework for Communication-Efficient Distributed Optimization (2016, background): “, by using error bound conditions (Necoara and Nedelcu, 2014; Wang and Lin, 2014), weak strong convexity conditions (Ma et al.”
- Linear Convergence of Randomized Feasible Descent Methods Under the Weak Strong Convexity Assumption (2016, background): “(See, for example, Devolder et al. 2014; Bonettini 2011; Tappenden et al. 2016; Hua and Yamashita 2012; Necoara and Nedelcu 2014b.) • Flexibility and wide applicability.”