Pradeep Chathuranga Weeraddana

Optimizing client association for load balancing and fairness in millimeter-wave wireless networks

Millimeter-wave communications in the 60-GHz band are considered one of the key technologies for enabling multigigabit wireless access. However, the special characteristics of such a band pose major obstacles to the optimal utilization of the wireless resources, where the problem of efficient client association to access points (APs) is of vital importance. In this paper, the client association in 60-GHz wireless access networks is investigated. The AP utilization and the quality of the rapidly vanishing communication links are the control parameters. Because of the tricky nonconvex and combinatorial nature of the client association optimization problem, a novel solution method is developed to guarantee balanced and fair resource allocation. A new distributed, lightweight, and easy-to-implement association algorithm, based on Lagrangian duality theory and subgradient methods, is proposed. It is shown that the algorithm is asymptotically optimal, that is, the relative duality gap diminishes to zero as the number of clients increases .

On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is, in general, difficult due to the nonconvexity of the problem. In this paper, two distributed solution methods that combine the fast convergence properties of augmented Lagrangian-based methods with the separability properties of alternating optimization are investigated. The first method is adapted from the classic quadratic penalty function method and is called the alternating direction penalty method (ADPM). Unlike the original quadratic penalty function method, where single-step optimizations are adopted, ADPM uses an alternating optimization which, in turn, makes it scalable. The second method is the well-known alternating direction method of multipliers (ADMM). It is shown that ADPM for nonconvex problems asymptotically converges to a primal feasible point under mild conditions and an additional condition ensuring that it asymptotically reaches the standard first-order necessary conditions for local optimality is introduced. In the case of the ADMM, novel sufficient conditions under which the algorithm asymptotically reaches the standard first-order necessary conditions are established. Based on this, complete convergence of the ADMM for a class of low-dimensional problems is characterized. Finally, the results are illustrated by applying ADPM and ADMM to a nonconvex localization problem in wireless-sensor networks.

A Distributed Approach for the Optimal Power-Flow Problem Based on ADMM and Sequential Convex Approximations

For operating electrical power networks, the Optimal Power Flow (OPF) problem plays a central role. The problem is nonconvex and NP hard. Therefore, designing efficient solution algorithms is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems for which zero duality holds, whereas for non-convex problems there is a lack of solution methods of provable performance. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated to each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically and numerically substantiated.

Weighted Sum-Rate Maximization in Wireless Networks: A Review

The weighted sum-rate maximization (WSRMax) problem plays a central role in many network control and optimization methods, such as power control, link scheduling, cross-layer control, network utility maximization. The problem is NP-hard in general. In Weighted Sum-Rate Maximization in Wireless Networks: A Review, a cohesive discussion of the existing solution methods associated with the WSRMax problem, including global, fast local, as well as decentralized methods is presented. In addition, general optimization approaches, such as branch and bound methods, complementary geometric programming, and decomposition methods, are discussed in depth to address the problem. Through a number of numerical examples, the applicability of the resulting algorithms in various application domains is demonstrated. The presented algorithms and the associated numerical results can be very useful for network engineers or researchers with an interest in network design.

Auction-Based Resource Allocation in MillimeterWave Wireless Access Networks

The resource allocation problem of optimal assignment of the stations to the available access points in 60 GHz millimeterWave wireless access networks is investigated. The problem is posed as a multi-assignment optimization problem. The proposed solution method converts the initial problem to a minimum cost flow problem and allows to design an efficient algorithm by a combination of auction algorithms. The solution algorithm exploits the network optimization structure of the problem, and thus is much more powerful than computationally intensive general-purpose solvers. Theoretical and numerical results evince numerous properties, such as optimality, convergence, and scalability in comparison to existing approaches.

Extensions of Fast-Lipschitz Optimization

The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying conditions, such as monotonicity of the objective function and contractivity of the constraints, have a unique optimal solution obtained via fast distributed algorithms that compute the fixed point of the constraints. This paper extends the set of problems for which the Fast-Lipschitz framework applies. Existing assumptions on the problem form are relaxed and new and generalized qualifying conditions are established by novel results based on Lagrangian duality. It is shown for which cases of more constraints than decision variables, and less constraints than decision variables Fast-Lipschitz optimization applies. New results are obtained by imposing non strict monotonicity of the objective functions. The extended Fast-Lipschitz framework is illustrated by a number of examples, including network optimization and optimal control problems.

Min-max fair car-parking slot assignment

Empirical studies show that cruising for car parking accounts for a non-negligible amount of the daily traffic, especially in central areas of large cities. Therefore, mechanisms for minimizing traffic from cruising directly affect the dynamics of traffic congestions. One way to minimizing cruising traffic is efficient car-parking-slot assignment. Usually, the related design problems are combinatorial and the worst-case complexity of optimal methods grows exponentially with the problem sizes. As a result, almost all existing methods for parking slot assignment are simple and greedy approaches, where each car or the user is assigned a free parking slot, which is closer to its destination. Moreover, no emphasis is placed to optimize any form of fairness among the users as the a social benefit. In this paper, the fairness as a metric for modeling the aggregate social benefit of the users is considered. An algorithm based on Lagrange duality is developed for car-parking-slot assignment. Numerical results illustrate the performance of the proposed algorithm compared to the optimal assignment and a greedy method.

On the convergence of an alternating direction penalty method for nonconvex problems

This paper investigates convergence properties of scalable algorithms for nonconvex and structured optimization. We consider a method that is adapted from the classic quadratic penalty function method, the Alternating Direction Penalty Method (ADPM). Unlike the original quadratic penalty function method, in which single-step optimizations are adopted, ADPM uses alternating optimization, which in turn is exploited to enable scalability of the algorithm. A special case of ADPM is a variant of the well known Alternating Direction Method of Multipliers (ADMM), where the penalty parameter is increased to infinity. We show that due to the increasing penalty, the ADPM asymptotically reaches a primal feasible point under mild conditions. Moreover, we give numerical evidence that demonstrates the potential of the ADPM for computing local optimal points when the penalty is not updated too aggressively.

Communication infrastructures in industrial automation: The case of 60 GHz millimeterWave communications

Wireless sensor networks for industrial automation applications must offer timely, reliable, and energy efficient communications at both low and high data rate. While traditional communication technologies between 2.4 GHz and 5 GHz are sometimes incapable to efficiently achieve the aforementioned goals, new communication strategies are emerging, such as millimeterWave communications. In this overview paper, the general requirements that factory and process automation impose on the network design are reviewed. Moreover, this paper presents and qualitatively evaluates the 60 GHz millimeterWave communication technology for automation. It is argued that the upcoming 60 GHz millimeterWave technology brings an enormous potential and can influence the design of the future communication infrastructures in factory and process automation.

A distributed approach for the optimal power flow problem

The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems where zero duality holds. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated to each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically substantiated. Finally, the proposed algorithm is evaluated on a number of test examples, where the convergence properties of the proposed algorithm are numerically substantiated and the performance is compared with a global optimal method.