Asynchronous Optimization Over Graphs: Linear Convergence Under Error Bound Conditions

Loris Cannelli

doi:10.1109/TAC.2020.3033490

Asynchronous Optimization Over Graphs: Linear Convergence Under Error Bound Conditions

2021-10-01

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Vyacheslav Kungurtsev

DOI：10.1109/TAC.2020.3033490

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We consider convex and nonconvex constrained optimization with a partially separable objective function: Agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables of that agent and those of a few others. This partitioned setting arises in several applications of practical interest. We propose what is, to the best of our knowledge, the first distributed, asynchronous algorithm with rate guarantees for this class of problems. When the objective function is nonconvex, the algorithm provably converges to a stationary solution at a sublinear rate whereas linear rate is achieved under the renowned Luo-Tseng error bound condition (which is less stringent than strong convexity). Numerical results on matrix completion and LASSO problems show the effectiveness of our method.

Keywords:

Delays

Optimization

Convergence

Partitioning algorithms

Nickel

Linear programming

Indexes

Asynchronous algorithms

error bounds

linear rate

multiagent systems

nonconvex optimization

Asynchronous Optimization Over Graphs: Linear Convergence Under Error Bound Conditions

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