Distributed Stochastic Power Control in Ad-hoc Networks: A Nonconvex Case

Utility-based power allocation in wireless ad-hoc networks is inherently nonconvex because of the global coupling induced by the co-channel interference. To tackle this challenge, we first show that the globally optimal point lies on the boundary of the feasible region, which is utilized as a basis to transform the utility maximization problem into an equivalent max-min problem with more structure. By using extended duality theory, penalty multipliers are introduced for penalizing the constraint violations, and the minimum weighted utility maximization problem is then decomposed into subproblems for individual users to devise a distributed stochastic power control algorithm, where each user stochastically adjusts its target utility to improve the total utility by simulated annealing. The proposed distributed power control algorithm can guarantee global optimality at the cost of slow convergence due to simulated annealing involved in the global optimization. The geometric cooling scheme and suitable penalty parameters are used to improve the convergence rate. Next, by integrating the stochastic power control approach with the back-pressure algorithm, we develop a joint scheduling and power allocation policy to stabilize the queueing systems. Finally, we generalize the above distributed power control algorithms to multicast communications, and show their global optimality for multicast traffic.Comment: Contains 12 pages, 10 figures, and 2 tables; work submitted to IEEE Transactions on Mobile Computin

Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems

We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multiuser interfering systems. Our main contributions are: i) the development of the first class of (inexact) Jacobi best-response algorithms with provable convergence, where all the users simultaneously and iteratively solve a suitably convexified version of the original sum-utility optimization problem; ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics; and iii) a framework that can be easily particularized to well-known applications, giving rise to very efficient practical (Jacobi or Gauss-Seidel) algorithms that outperform existing adhoc methods proposed for very specific problems. Interestingly, our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many blockcoordinate descent schemes for convex functions.Comment: submitted to IEEE Transactions on Signal Processin

Layering as Optimization Decomposition: Questions and Answers

Network protocols in layered architectures have historically been obtained on an ad-hoc basis, and much of the recent cross-layer designs are conducted through piecemeal approaches. Network protocols may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems in the form of generalized Network Utility Maximization (NUM), providing insight on what they optimize and on the structures of network protocol stacks. In the form of 10 Questions and Answers, this paper presents a short survey of the recent efforts towards a systematic understanding of "layering" as "optimization decomposition". The overall communication network is modeled by a generalized NUM problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. Furthermore, there are many alternative decompositions, each leading to a different layering architecture. Industry adoption of this unifying framework has also started. Here we summarize the current status of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and coding. We also discuss under-explored future research directions in this area. More importantly than proposing any particular crosslayer design, this framework is working towards a mathematical foundation of network architectures and the design process of modularization

Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks

We study nonconvex distributed optimization in multiagent networks where the communications between nodes is modeled as a time-varying sequence of arbitrary digraphs. We introduce a novel broadcast-based distributed algorithmic framework for the (constrained) minimization of the sum of a smooth (possibly nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on Successive Convex Approximation (SCA) techniques coupled with i) a tracking mechanism instrumental to locally estimate the gradients of agents' cost functions; and ii) a novel broadcast protocol to disseminate information and distribute the computation among the agents. Asymptotic convergence to stationary solutions is established. A key feature of the proposed algorithm is that it neither requires the double-stochasticity of the consensus matrices (but only column stochasticity) nor the knowledge of the graph sequence to implement. To the best of our knowledge, the proposed framework is the first broadcast-based distributed algorithm for convex and nonconvex constrained optimization over arbitrary, time-varying digraphs. Numerical results show that our algorithm outperforms current schemes on both convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA, US

Consistent Sensor, Relay, and Link Selection in Wireless Sensor Networks

In wireless sensor networks, where energy is scarce, it is inefficient to have all nodes active because they consume a non-negligible amount of battery. In this paper we consider the problem of jointly selecting sensors, relays and links in a wireless sensor network where the active sensors need to communicate their measurements to one or multiple access points. Information messages are routed stochastically in order to capture the inherent reliability of the broadcast links via multiple hops, where the nodes may be acting as sensors or as relays. We aim at finding optimal sparse solutions where both, the consistency between the selected subset of sensors, relays and links, and the graph connectivity in the selected subnetwork are guaranteed. Furthermore, active nodes should ensure a network performance in a parameter estimation scenario. Two problems are studied: sensor and link selection; and sensor, relay and link selection. To solve such problems, we present tractable optimization formulations and propose two algorithms that satisfy the previous network requirements. We also explore an extension scenario: only link selection. Simulation results show the performance of the algorithms and illustrate how they provide a sparse solution, which not only saves energy but also guarantees the network requirements.Comment: 27 pages, 17 figure