82 research outputs found
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
Optimization and Control of Communication Networks
Recently, there has been a surge in research activities that utilize the power of recent developments in nonlinear
optimization to tackle a wide scope of work in the analysis and design of communication systems, touching every
layer of the layered network architecture, and resulting in both intellectual and practical impacts significantly
beyond the earlier frameworks. These research activities are driven by both new demands in the areas of
communications and networking, and new tools emerging from optimization theory. Such tools include new
developments of powerful theories and highly efficient computational algorithms for nonlinear convex
optimization, as well as global solution methods and relaxation techniques for nonconvex optimization.
Optimization theory can be used to analyze, interpret, or design a communication system, for both forward-engineering and reverse-engineering. Over the last few years, it has been successfully applied to a wide range of
communication systems, from the high speed Internet core to wireless networks, from coding and equalization to
broadband access, and from information theory to network topology models. Some of the theoretical advances
have also been put into practice and started making visible impacts, including new versions of TCP congestion
control, power control and scheduling algorithms in wireless networks, and spectrum management in DSL
broadband access networks.
Under the theme of optimization and control of communication networks, this Hot Topic Session consists of five
invited talks covering a wide range of issues, including protocols, pricing, resource allocation, cross layer design,
traffic engineering in the Internet, optical transport networks, and wireless networks
A Unified Successive Pseudo-Convex Approximation Framework
In this paper, we propose a successive pseudo-convex approximation algorithm
to efficiently compute stationary points for a large class of possibly
nonconvex optimization problems. The stationary points are obtained by solving
a sequence of successively refined approximate problems, each of which is much
easier to solve than the original problem. To achieve convergence, the
approximate problem only needs to exhibit a weak form of convexity, namely,
pseudo-convexity. We show that the proposed framework not only includes as
special cases a number of existing methods, for example, the gradient method
and the Jacobi algorithm, but also leads to new algorithms which enjoy easier
implementation and faster convergence speed. We also propose a novel line
search method for nondifferentiable optimization problems, which is carried out
over a properly constructed differentiable function with the benefit of a
simplified implementation as compared to state-of-the-art line search
techniques that directly operate on the original nondifferentiable objective
function. The advantages of the proposed algorithm are shown, both
theoretically and numerically, by several example applications, namely, MIMO
broadcast channel capacity computation, energy efficiency maximization in
massive MIMO systems and LASSO in sparse signal recovery.Comment: submitted to IEEE Transactions on Signal Processing; original title:
A Novel Iterative Convex Approximation Metho
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
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