A penalty ADMM with quantized communication for distributed optimization over multi-agent systems

Chenyang Liu; Xiaohua Dou; Yuan Fan; Songsong Cheng

Displaying similar documents to “A penalty ADMM with quantized communication for distributed optimization over multi-agent systems”

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This paper investigates a distributed algorithm for the multi-agent constrained optimization problem, which is to minimize a global objective function formed by a sum of local convex (possibly nonsmooth) functions under both coupled inequality and affine equality constraints. By introducing auxiliary variables, we decouple the constraints and transform the multi-agent optimization problem into a variational inequality problem with a set-valued monotone mapping. We propose a distributed...

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The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of $β_{k}^{R M I L}$ and $β_{k}^{H S}$ . We compute the convex parameter $θ_{k}$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments...

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In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable...

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Locally Lipschitz vector optimization with inequality and equality constraints

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The present paper studies the following constrained vector optimization problem: ${min}_{C} f (x)$ , $g (x) \in - K$ , $h (x) = 0$ , where $f : ℝ^{n} \to ℝ^{m}$ , $g : ℝ^{n} \to ℝ^{p}$ are locally Lipschitz functions, $h : ℝ^{n} \to ℝ^{q}$ is $C^{1}$ function, and $C \subset ℝ^{m}$ and $K \subset ℝ^{p}$ are closed convex cones. Two types of solutions are important for the consideration, namely $w$ -minimizers (weakly efficient points) and $i$ -minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point $x^{0}$ to be a $w$ -minimizer and first-order sufficient conditions...

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Parametric control to quasi-linear systems based on dynamic compensator and multi-objective optimization

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A stochastic mirror-descent algorithm for solving $A X B = C$ over an multi-agent system

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In this paper, we consider a distributed stochastic computation of $A X B = C$ with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of $A X B = C$ , we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm....

The adaptation of the $k$ -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

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Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate

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This paper proposes a distributed accelerated first-order continuous-time algorithm for $O (1 / t^{2})$ convergence to Nash equilibria in a class of two-subnetwork zero-sum games with bilinear couplings. First-order methods, which only use subgradients of functions, are frequently used in distributed/parallel algorithms for solving large-scale and big-data problems due to their simple structures. However, in the worst cases, first-order methods for two-subnetwork zero-sum games often have an asymptotic...