13 research outputs found
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
Distributed Algorithms for Computing a Fixed Point of Multi-Agent Nonexpansive Operators
This paper investigates the problem of finding a fixed point for a global
nonexpansive operator under time-varying communication graphs in real Hilbert
spaces, where the global operator is separable and composed of an aggregate sum
of local nonexpansive operators. Each local operator is only privately
accessible to each agent, and all agents constitute a network. To seek a fixed
point of the global operator, it is indispensable for agents to exchange local
information and update their solution cooperatively. To solve the problem, two
algorithms are developed, called distributed Krasnosel'ski\u{\i}-Mann (D-KM)
and distributed block-coordinate Krasnosel'ski\u{\i}-Mann (D-BKM) iterations,
for which the D-BKM iteration is a block-coordinate version of the D-KM
iteration in the sense of randomly choosing and computing only one
block-coordinate of local operators at each time for each agent. It is shown
that the proposed two algorithms can both converge weakly to a fixed point of
the global operator. Meanwhile, the designed algorithms are applied to recover
the classical distributed gradient descent (DGD) algorithm, devise a new
block-coordinate DGD algorithm, handle a distributed shortest distance problem
in the Hilbert space for the first time, and solve linear algebraic equations
in a novel distributed approach. Finally, the theoretical results are
corroborated by a few numerical examples
Distributed Stochastic Subgradient Optimization Algorithms Over Random and Noisy Networks
We study distributed stochastic optimization by networked nodes to
cooperatively minimize a sum of convex cost functions. The network is modeled
by a sequence of time-varying random digraphs with each node representing a
local optimizer and each edge representing a communication link. We consider
the distributed subgradient optimization algorithm with noisy measurements of
local cost functions' subgradients, additive and multiplicative noises among
information exchanging between each pair of nodes. By stochastic Lyapunov
method, convex analysis, algebraic graph theory and martingale convergence
theory, it is proved that if the local subgradient functions grow linearly and
the sequence of digraphs is conditionally balanced and uniformly conditionally
jointly connected, then proper algorithm step sizes can be designed so that all
nodes' states converge to the global optimal solution almost surely