1 edition of The dual decomposition method and its application to an interdicted network found in the catalog.
The dual decomposition method and its application to an interdicted network
Timothy Paul Gannon
by Naval Postgraduate School, Available from the National Technical Information Service in Monterey, Calif, Springfield, Va
Written in English
|Contributions||Bailey, Michael P.|
|The Physical Object|
|Number of Pages||66|
The Lagrangian dual (8) is a concave, nonsmooth optimization problem, which Car˝e and Schultz  propose to solve with subgradient methods (or more properly in this context, supergradient methods). The bounds generated from the Lagrangian dual are used within a branch-and-bound procedure. This is the so-called dual decomposition (DD) approach. We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The network users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users’ requirements. This approach leads to a convex optimization problem with balance and capacity constraints.
imaging application. Inspired by its impressive potential, we developed a new Butterfly network to perform the image domain dual material decomposition due to its strong approximation ability to the mapping functions in DECT. Methods: The Butterfly network is derived from the image domain DECT decomposition. Chapter 11 Decomposition Techniques Introduction. In this chapter, we focus on the application of decomposition techniques to network optimization problems. A problem decomposition is a transformation of a problem into a set of, potentially, many independent and simpler problems, coordinated by a so-called master program, such that the optimum solution of this overall scheme also .
results obtained with the method. Although we discuss its application to domain decomposition, the same technique is also suited for other applications, e.g., • to handle diﬀusion terms in the discontinuous Galerkin method [2,6]; • to simplify mesh generation (diﬀerent parts can be meshed independently from each other);. A method to solve the design of a distribution network for bottled drinks company is introduced. The distribution network proposed includes three stages: manufacturing centers, consolidation centers using cross-docking, and distribution centers. The problem is formulated using a mixed-integer programming model in the deterministic and single period contexts.
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Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection The dual decomposition method and its application to an interdicted network. Approved for public release; distribution is unlimitedThis paper introduces the dual decomposition method for determining the distribution of an optimal objective function for a network problem.
The objective function is to minimize the shortfall of demands to prioritized sinks for a four day period over a network that is subject to : Timothy Paul Gannon.
In recent years, the technique of dual decomposition, also called Lagrangian relaxation, has proven to be a powerful means of solving these inference problems by decomposing them into simpler components that are repeatedly solved independently and combined into a global by: A Tutorial on Decomposition Methods for Network Utility Maximization Daniel P.
Palomar, Member, IEEE, and Mung Chiang, Member, IEEE Tutorial Paper Abstract—A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation.
It helps us obtain the mostCited by: Shortest-path network interdiction, where a defender strategically allocates interdiction resource on the arcs or nodes in a network and an attacker traverses the capacitated network along a shortest s-t path from a source to a terminus, is an important research problem with potential real-world impact.
In this paper, based on game-theoretic methodologies, we consider a novel stochastic Cited by: 1. Qingjiang Shi and Mingyi Hong, “Penalty Dual Decomposition Method With Its Application in Signal Processing”, Proc.
ICASSP Songtao Lu, Mingyi Hong and Zhengdao Wang, “A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization”, Proc. ICASSP dual nature of domain decomposition methods. They are solvers of linear systems keeping in mind that the matrices arise from the discretization of partial di erential operators.
As for domain decomposition methods that directly address non linearities, we refer the. – gradient or Newton method (if φi diﬀerentiable) – subgradient, cutting-plane, or ellipsoid method • each iteration of master problem requires solving the two subproblems (in parallel) • if master algorithm converges fast enough and subproblems are suﬃciently easier to solve than original problem, we get savings EEb, Stanford.
Dual decomposition and Lagrangian relaxation For the MAP inference problem: MAP() = max x (X i2V i(xi) + X f2F f(x f)) for any given factor f, we make copy of each variables xi in the factor and denote as xf i.
8 Introduction to Dual Decomposition for Inference x 1 x 2 x 3 x 4. f(x 1,x 2). h(x 2,x 4). k(x 3,x 4). g(x 1,x 3) x1. f 2(x 2)!f 1(x. Theory of Probability & Its Applications. Browse TVP; FAQ; E-books. Browse e-books; Series Descriptions; Book Program; MARC Records; FAQ; Proceedings; For Authors.
Journal Author Submissions; Book Author Submissions; Subscriptions. Journal Subscription; Journal Pricing; Journal Subscription Agreement; E-book Subscription; E-book Purchase; E. The book is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods.
It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms.
Farkas’ Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method.
Dantzig-Wolfe decomposition, and a primal-dual. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different.
The separability of the constraints and objective function is an underlying assumption in the LR decomposition method. The drawback of the LR method is that, if the overall problem is nonconvex, the solution of the dual problem obtained in the LR decomposition method is possibly not the same as for the primal problem.
A neural network-based method for spectral network, material decomposition (Some figures may appear in colour only in the online journal) 1. Introduction Computed tomography (CT) has been the dominant modality for imaging in both clini-cal and pre-clinical applications due to its very high spatial and temporal resolution.
() Rate Analysis of Inexact Dual First-Order Methods Application to Dual Decomposition. IEEE Transactions on Automatic Control() Accelerated Dual Descent for Network. Efficiently transmitting data in wireless networks requires joint optimization of routing, scheduling, and power control.
As opposed to the universal dual decomposition we present a method that solves this optimization problem by fully exploiting our knowledge of active constraints. The method still maintains main requirements such as optimality, distributed implementation, multiple path.
Primal Decomposition When zis discrete and can take values from only a small set: each z I Solve the two subproblems and compute objective the zwith the minimum objective Example Loopy graph Two chains.
The decomposition method above is presented as an example. For the ED problem, other decomposition techniques exist that have been successfully applied and we encourage the readers to investigate them.
For example, dual decomposition, alternating direction method of multipliers, Dantzig-Wolfe reformulation, etc. Stochastic Approaches. Dual rst-order methods Even if we can’t derive dual (conjugate) in closed form, we can still usedual-based gradientorsubgradientmethods Consider the problem min x f(x) subject to Ax= b Its dual problem is max u f (ATu) bTu where f is conjugate of f.
De ning g(u) =. The unique planar embedding of a cycle graph divides the plane into only two regions, the inside and outside of the cycle, by the Jordan curve r, in an n-cycle, these two regions are separated from each other by n different edges.
Therefore, the dual graph of the n-cycle is a multigraph with two vertices (dual to the regions), connected to each other by n dual edges. In this paper, we propose a dual-decomposition based distributed optimization algorithm for WSNs. The goal is to optimize a global objective function which is a combination of local objective functions known by the sensors only.
A gradient-based algorithm is proposed to find the approximate solution for the dual problem.The Goal A Mathematical Theory of Network Architectures † Particular focus on the architectures of layering and distributed control † There are also boundaries to the use of mathematical approach to the economics, psychology, and engineering of network architectures † But certainly provides rigorous approaches on why protocols work, when it will not work, and how to make it work better.