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We consider continuous-time dynamics for distributed optimization with set constraints in the note. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with projection, we propose a distributed projection-free dynamics by employing the Frank-Wolfe method, also known as the conditional gradient algorithm. The process searches a feasible descent direction with solving an alternative linear optimization instead of a quadratic one. To make the algorithm implementable over weight-balanced digraphs, we design one dynamics for the consensus of local decision variables and another dynamics of auxiliary variables to track the global gradient. Then we prove the convergence of the dynamical systems to the optimal solution, and provide detailed numerical comparisons with both projection-based dynamics and other distributed projection-free algorithms.
The Frank-Wolfe method solves smooth constrained convex optimization problems at a generic sublinear rate of $mathcal{O}(1/T)$, and it (or its variants) enjoys accelerated convergence rates for two fundamental classes of constraints: polytopes and st
In this paper, we propose a new method based on the Sliding Algorithm from Lan(2016, 2019) for the convex composite optimization problem that includes two terms: smooth one and non-smooth one. Our method uses the stochastic noised zeroth-order oracle
We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic Riemannian Fra
Distributed optimization is concerned with using local computation and communication to realize a global aim of optimizing the sum of local objective functions. It has gained wide attention for a variety of applications in networked systems. This pap
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is defined as t