41 research outputs found
Distributed Online Optimization with Coupled Inequality Constraints over Unbalanced Directed Networks
This paper studies a distributed online convex optimization problem, where
agents in an unbalanced network cooperatively minimize the sum of their
time-varying local cost functions subject to a coupled inequality constraint.
To solve this problem, we propose a distributed dual subgradient tracking
algorithm, called DUST, which attempts to optimize a dual objective by means of
tracking the primal constraint violations and integrating dual subgradient and
push sum techniques. Different from most existing works, we allow the
underlying network to be unbalanced with a column stochastic mixing matrix. We
show that DUST achieves sublinear dynamic regret and constraint violations,
provided that the accumulated variation of the optimal sequence grows
sublinearly. If the standard Slater's condition is additionally imposed, DUST
acquires a smaller constraint violation bound than the alternative existing
methods applicable to unbalanced networks. Simulations on a plug-in electric
vehicle charging problem demonstrate the superior convergence of DUST
Push-Pull Based Distributed Primal-Dual Algorithm for Coupled Constrained Convex Optimization in Multi-Agent Networks
This paper focuses on a distributed coupled constrained convex optimization
problem over directed unbalanced and time-varying multi-agent networks, where
the global objective function is the sum of all agents' private local objective
functions, and decisions of all agents are subject to coupled equality and
inequality constraints and a compact convex subset. In the multi-agent
networks, each agent exchanges information with other neighboring agents.
Finally, all agents reach a consensus on decisions, meanwhile achieving the
goal of minimizing the global objective function under the given constraint
conditions. For the purpose of protecting the information privacy of each
agent, we first establish the saddle point problem of the constrained convex
optimization problem considered in this article, then based on the push-pull
method, develop a distributed primal-dual algorithm to solve the dual problem.
Under Slater's condition, we will show that the sequence of points generated by
the proposed algorithm converges to a saddle point of the Lagrange function.
Moreover, we analyze the iteration complexity of the algorithm
Distributed Aggregative Optimization over Multi-Agent Networks
This paper proposes a new framework for distributed optimization, called
distributed aggregative optimization, which allows local objective functions to
be dependent not only on their own decision variables, but also on the average
of summable functions of decision variables of all other agents. To handle this
problem, a distributed algorithm, called distributed gradient tracking (DGT),
is proposed and analyzed, where the global objective function is strongly
convex, and the communication graph is balanced and strongly connected. It is
shown that the algorithm can converge to the optimal variable at a linear rate.
A numerical example is provided to corroborate the theoretical result
Implicit Tracking-based Distributed Constraint-coupled Optimization
A class of distributed optimization problem with a globally coupled equality
constraint and local constrained sets is studied in this paper. For its special
case where local constrained sets are absent, an augmented primal-dual gradient
dynamics is proposed and analyzed, but it cannot be implemented distributedly
since the violation of the coupled constraint needs to be used. Benefiting from
the brand-new comprehending of a classical distributed unconstrained
optimization algorithm, the novel implicit tracking approach is proposed to
track the violation distributedly, which leads to the birth of the
\underline{i}mplicit tracking-based \underline{d}istribut\underline{e}d
\underline{a}ugmented primal-dual gradient dynamics (IDEA). A projected variant
of IDEA, i.e., Proj-IDEA, is further designed to deal with the general case
where local constrained sets exist. With the aid of the Lyapunov stability
theory, the convergences of IDEA and Pro-IDEA over undigraphs and digraphs are
analyzed respectively. As far as we know, Proj-IDEA is the first constant
step-size distributed algorithm which can solve the studied problem without the
need of the strict convexity of local cost functions. Besides, if local cost
functions are strongly convex and smooth, IDEA can achieve exponential
convergence with a weaker condition about the coupled constraint. Finally,
numerical experiments are taken to corroborate our theoretical results.Comment: in IEEE Transactions on Control of Network Systems, 202
Distributed Online Convex Optimization with an Aggregative Variable
This paper investigates distributed online convex optimization in the
presence of an aggregative variable without any global/central coordinators
over a multi-agent network, where each individual agent is only able to access
partial information of time-varying global loss functions, thus requiring local
information exchanges between neighboring agents. Motivated by many
applications in reality, the considered local loss functions depend not only on
their own decision variables, but also on an aggregative variable, such as the
average of all decision variables. To handle this problem, an Online
Distributed Gradient Tracking algorithm (O-DGT) is proposed with exact gradient
information and it is shown that the dynamic regret is upper bounded by three
terms: a sublinear term, a path variation term, and a gradient variation term.
Meanwhile, the O-DGT algorithm is also analyzed with stochastic/noisy
gradients, showing that the expected dynamic regret has the same upper bound as
the exact gradient case. To our best knowledge, this paper is the first to
study online convex optimization in the presence of an aggregative variable,
which enjoys new characteristics in comparison with the conventional scenario
without the aggregative variable. Finally, a numerical experiment is provided
to corroborate the obtained theoretical results