An augmented Lagrangian method for distributed optimization

Huang

IEEE Trans. on Mobile Comput.

2021

Wireless power transfer (WPT) technology enables a cost-effective and sustainable energy supply in wireless networks. However, the broadcast nature of wireless signals makes them non-excludable public goods, which leads to potential free-riders among energy receivers. In this study, we formulate the wireless power provision problem as a public goods provision problem, aiming to maximize the social welfare of a system of an energy transmitter (ET) and all the energy users (EUs), while considering their private information and self-interested behaviors. We propose a two-phase all-or-none scheme involving a low-complexity Power And Taxation (PAT) mechanism, which ensures voluntary participation, truthfulness, budget balance, and social optimality at every Nash equilibrium (NE). We propose a distributed PAT (D-PAT) algorithm to reach an NE, and prove its convergence by connecting the structure of NEs and that of the optimal solution to a related optimization problem. We further extend the analysis to a multi-channel system, which brings a further challenge due to the non-strict concavity of the agents' payoffs. We propose a Multi-Channel PAT (M-PAT) mechanism and a distributed M-PAT (D-MPAT) algorithm to address the challenge. Simulation results show that, our design is most beneficial when there are more EUs with more homogeneous channel gains.

Section: Distributed Pure Optimization (Dpo) Algorithmmentioning

confidence: 99%

“…To show that Algorithm 2 is an ADAL-based algorithm, we consider the augmented Lagrangian function of the R-SWM-M Problem with the following decomposable structures [47]:…”

Section: Lagrangian and Augmented Lagrangianmentioning

confidence: 99%

See 1 more Smart Citation

Wireless Power Transfer with Information Asymmetry: A Public Goods Perspective

Huang

IEEE Trans. on Mobile Comput.

2021

“…As such, distributed algorithms avoid the cost and fragility associated with centralized coordination, and provide better privacy for the autonomous decision makers. Popular distributed optimization methods in the literature include distributed subgradient methods [4], [5], dual averaging methods [6], and augmented Lagrangian methods [7]- [10]. Yan The above distributed optimization methods usually assume a static objective function.…”

Section: Introductionmentioning

confidence: 99%

A Distributed Online Convex Optimization Algorithm with Improved Dynamic Regret

2019 IEEE 58th Conference on Decision and Control (CDC)

Ravier

Zavlanos

et al. 2019

Self Cite

We consider the problem of distributed online convex optimization, where a group of agents collaborate to track the trajectory of the global minimizers of sums of time-varying objective functions in an online manner. For general convex functions, the theoretical upper bounds of existing methods are given in terms of regularity measures associated with the dynamical system as well as the time horizon. It is thus of interest to determine whether the explicit time horizon dependence can be removed as in the case of centralized optimization. In this work, we propose a novel distributed online gradient descent algorithm and show that the dynamic regret bound of this algorithm has no explicit dependence on the time horizon. Instead, it depends on a new regularity measure quantifying the total change in gradients at the optimal points at each time. The main driving force of our algorithm is an online adaptation of the gradient tracking technique used in static optimization. Since, in many applications, time-varying objective functions and the corresponding optimal points follow a non-adversarial dynamical system, we also consider the role of prediction assuming that the optimal points evolve according to a linear dynamical system. We present numerical experiments that show that our proposed algorithm outperforms the existing distributed mirror descentbased state of the art methods in term of the optimizer tracking performance. We also present an empirical example suggesting that the analysis of our algorithm is optimal in the sense that the regularity measures in the theoretical bounds cannot be removed.

“…For such f , (1.2) is often true, for instance because U k is compact and finite bounds −∞ < u k ≤ u k ≤ū k < ∞ are known for each u k ∈ U k (very often, U k ⊆ {0, 1} n k ). Minimizing f solves the Lagrangian dual of (1.3), which has countless applications; e.g., [4,5,12,16,17,24,27] among the many others. Typically (1.3) is "difficult", due to either being largescale, N P-hard, or both.…”

Section: Introductionmentioning

confidence: 99%

Incremental Bundle Methods using Upper Models

Ackooij¹,

Frangioni²

2018

SIAM J. Optim.

We propose a family of proximal bundle methods for minimizing sum-structured convex nondifferentiable functions which require two slightly uncommon assumptions, that are satisfied in many relevant applications: Lipschitz continuity of the functions and oracles which also produce upper estimates on the function values. In exchange, the methods: i) use upper models of the functions that allow to estimate function values at points where the oracle has not been called; ii) provide the oracles with more information about when the function computation can be interrupted, possibly diminishing their cost; iii) allow to skip oracle calls entirely for some of the component functions, not only at "null steps" but also at "serious steps"; iv) provide explicit and reliable a-posteriori estimates of the quality of the obtained solutions; v) work with all possible combinations of different assumptions on the oracles. We also discuss introduction of constraints (or, more generally, of easy components) and use of (partly) aggregated models.