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105
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods
 SIAM REVIEW VOL. 45, NO. 3, PP. 385–482
, 2003
"... Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked ..."
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Cited by 222 (15 self)
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Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints and linear constraints. We also discuss extensions to problems with nonlinear constraints.
Residual belief propagation: Informed scheduling for asynchronous message passing
 in Proceedings of the Twentysecond Conference on Uncertainty in AI (UAI
, 2006
"... Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, reallife inference tasks. While it is widely recognized that ..."
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Cited by 113 (3 self)
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Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, reallife inference tasks. While it is widely recognized that the scheduling of messages in these algorithms may have significant consequences, this issue remains largely unexplored. In this work, we address the question of how to schedule messages for asynchronous propagation so that a fixed point is reached faster and more often. We first show that any reasonable asynchronous BP converges to a unique fixed point under conditions similar to those that guarantee convergence of synchronous BP. In addition, we show that the convergence rate of a simple roundrobin schedule is at least as good as that of synchronous propagation. We then propose residual belief propagation (RBP), a novel, easytoimplement, asynchronous propagation algorithm that schedules messages in an informed way, that pushes down a bound on the distance from the fixed point. Finally, we demonstrate the superiority of RBP over stateoftheart methods for a variety of challenging synthetic and reallife problems: RBP converges significantly more often than other methods; and it significantly reduces running time until convergence, even when other methods converge. 1
Solution of Partial Differential Equations on Vector Computers
 Proc. 1977 Army Numerical Analysis and Computers Conference
, 1977
"... In this paper we review the present status of numerical methods for partial differential equations on vector and parallel computers. A discussion of the relevant aspects of these computers and a brief review of their development is included, with particular attention paid to those characteristics t ..."
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Cited by 64 (0 self)
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In this paper we review the present status of numerical methods for partial differential equations on vector and parallel computers. A discussion of the relevant aspects of these computers and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selecUon. Both direct and iteraUve methods are given for elliptic equations as well as explicit and implicit methods for initialboundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restricUons or the lack of adequate algorithms. A brief discussion of application areas utilizing these computers is included.
Pricing, Provisioning and Peering: Dynamic Markets for Differentiated Internet Services and Implications for Network Interconnections
 IEEE Journal on Selected Areas in Communications
, 2000
"... This paper presents a decentralized auctionbased approach to pricing of edgeallocated bandwidth in a differentiated services Internet. The players in our network economy model are one rawcapacity seller per network, one broker per service per network, and users, to play the roles of wholesellers ..."
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Cited by 57 (0 self)
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This paper presents a decentralized auctionbased approach to pricing of edgeallocated bandwidth in a differentiated services Internet. The players in our network economy model are one rawcapacity seller per network, one broker per service per network, and users, to play the roles of wholesellers, retailers, and endbuyers, respectively, in a twotier wholeseller/retailer market, which is best interpreted as a "senderpay" model. With the progressive second price auction mechanism as the basic building block, we conduct a game theoretic analysis, deriving optimal strategies for buyers and brokers, and show the existence of networkwide market equilibria.
Distributed Pagerank for P2P Systems
, 2003
"... This paper defines and describes a fully distributed implementation of Google's highly effective Pagerank algorithm, for "peer to peer"(P2P) systems. The implementation is based on chaotic (asynchronous) iterative solution of linear systems. The P2P implementation also enables increme ..."
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Cited by 50 (7 self)
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This paper defines and describes a fully distributed implementation of Google's highly effective Pagerank algorithm, for "peer to peer"(P2P) systems. The implementation is based on chaotic (asynchronous) iterative solution of linear systems. The P2P implementation also enables incremental computation of pageranks as new documents are entered into or deleted from the network. Incremental update enables continuously accurate pageranks whereas the currently centralized web crawl and computation over Internet documents requires several days. This suggests possible applicability of the distributed algorithm to pagerank computations as a replacement for the centralized web crawler based implementation for Internet documents. A complete solution of the distributed pagerank computation for an inplace network converges rapidly (1% accuracy in 10 iterations) for large systems although the time for an iteration may be long. The incremental computation resulting from addition of a single document converges extremely rapidly, typically requiring update path lengths of under 15 nodes even for large networks and very accurate solutions.
Adaptive aggregation methods for infinite horizon dynamic programming
 IEEE Trasactions on Automatic Control
, 1989
"... We propose a class of iterative aggregation algorithms for solving infinite horizon dynamic programming problems. The idea is to interject aggregation iterations in the course of the usual successive approximation method. An important new feature that sets our method apart from earlier proposals is ..."
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Cited by 48 (1 self)
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We propose a class of iterative aggregation algorithms for solving infinite horizon dynamic programming problems. The idea is to interject aggregation iterations in the course of the usual successive approximation method. An important new feature that sets our method apart from earlier proposals is that the aggregate groups of states change adaptively from one aggregation iteration to the next, depending on the progress of the computation. This allows acceleration of convergence in difficult problems involving multiple ergodic classes for which methods using fixed groups of aggregate states are ineffective. No knowledge of special problem structure is utilized by the algorithms. Consider a Markov chain with finite state space S = { 1,...,n}. Let x(t) denote the state of the chain at stage t. Assume that there is a finite decision space U, and that, for each state x(t) and decision u(t) at stage t, the state transition probabilities are given and are independent of t. Let oa E (0,1) be a discount factor and g(x(t), u(t)) be a given cost function of state and
Market Mechanisms for Network Resource Sharing
, 1999
"... The theme of this thesis is the design and analysis of decentralized and distributed market mechanisms for resource sharing in multiservice networks. The motivation for a marketbased approach is twofold. First, in modern multiservice networks, resources such as bandwidth and buffer space have dif ..."
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Cited by 45 (7 self)
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The theme of this thesis is the design and analysis of decentralized and distributed market mechanisms for resource sharing in multiservice networks. The motivation for a marketbased approach is twofold. First, in modern multiservice networks, resources such as bandwidth and buffer space have different value to different users, and these valuations cannot, in general, be accurately known in advance as users compete against each other for the resources. Second, the network resources themselves are distributed, and often, not subject to any single authority. We present
Synchronized and Asynchronous Parallel Algorithms for Multiprocessors," Algorithms and Complexity
"... algorithms for multiprocessors ..."
The Application of Microeconomics to the Design of Resource Allocation and Control Algorithms
, 1989
"... In this thesis, we present a new methodology for resource sharing algorithms in distributed systems. We propose that a distributed computing system should be composed of a decentralized community of microeconomic agents. We show that this approach decreases complexity and can substantially improve ..."
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Cited by 22 (4 self)
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In this thesis, we present a new methodology for resource sharing algorithms in distributed systems. We propose that a distributed computing system should be composed of a decentralized community of microeconomic agents. We show that this approach decreases complexity and can substantially improve performance. We compare the performance, generality and complexity of our algorithms with noneconomic algorithms. To validate the usefulness of our approach, we present economies that solve three distinct resource management problems encountered in large, distributed systems. The first economy performs CPU load balancing and demonstrates how our approach limits complexity and effectively allocates resources when compared to noneconomic algorithms. We show that the economy achieves better performance than a representative noneconomic algorithm. The load balancing economy spa...