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SYNCHRONOUS AND ASYNCHRONOUS IMPLEMENTATIONS OF relaxation algorithms FOR NONLINEAR NETWORK OPTIMIZATION

PARALLEL COMPUTING 1991年第8期17卷 873-894页

作者： CHAJAKIS, ED ZENIOS, SA Decision Sciences Department The Wharton School University of Pennsylvania Philadelphia PA 19104 USA

We discuss a parallel dual relaxation algorithm for network optimization. Synchronous and asynchronous implementations of the algorithm are developed on a shared memory multiprocessor, the Alliant FX/8. Alternative designs for parallel computing that tradeoff synchronization delays with computations are proposed. Their performance is analyzed empirically with computational experiments. It is demonstrated that the most effective parallel implementation is an asynchronous one, for which speedup factors of up to 7.2 are achieved on an 8 processor system.

关键词： NONLINEAR NETWORK OPTIMIZATION relaxation algorithms PARALLEL IMPLEMENTATION PARTITIONING SCHEDULING SYNCHRONIZATION SHARED MEMORY MULTIPROCESSOR

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An all-linear programming relaxation algorithm for optimizing over the efficient set

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Journal of Global Optimization 1991年第1期1卷 83-104页

作者： Benson, Harold P. College of Business Administration University of Florida Gainesville 32611-2017 Florida United States

The problem (P) of optimizing a linear function over the efficient set of a multiple objective linear program has many important applications in multiple criteria decision making. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. Perhaps due to its inherent difficulty, it appears that no precisely-delineated implementable algorithm exists for solving problem (P) globally. In this paper a relaxation algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact optimal solution to the problem after a finite number of iterations. A detailed discussion is included of how to implement the algorithm using only linear programming methods. Convergence of the algorithm is proven, and a sample problem is solved. © 1991 Kluwer Academic Publishers.

关键词： efficient set Global optimization multiple criteria decision making multiple objective linear programming relaxation algorithms

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ON THE DYNAMICS OF MEMORIZATION PROCESSES

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NEURAL NETWORKS 1988年第4期1卷 309-322页

作者： PERETTO, P HEBREW UNIV JERUSALEM INST ADV STUDIESJERUSALEMISRAEL

Learning can be considered as an optimization problem which is solved either by using a linear programming algorithm or by using a relaxation algorithm. Both approaches appeal to the same hypotheses. The linear programming algorithm has been introduced by Krauth and Mezard. Here we study learning rules based on relaxation algorithms which do not use strict constraints on the norm of efficacies but only boundary constraints. The algorithm comes in the form of an Hebbian rule weighted by a factor which hinders the memorization of already well imprinted patterns. We show that the norm either increases steadily up to its limit if M < 2·N (the Venkatesh limit) or remains finite if M > 2·N. This property allows the system to be never stuck into overcrowding conditions making it reusable for long-term memory even though it used to be overcrowded at a given moment in its history. It also accounts for palimpsest effects. Possible biological implementations are discussed. Finally the algorithm is easily generalized to systems comprising hidden units.

关键词： Learning dynamics relaxation algorithms Optimal memorization Long-term memories short-term memories Reusable memory Learning in networks comprising hidden units

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A CLASS OF INHERENTLY FAULT TOLERANT DISTRIBUTED PROGRAMS

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IEEE TRANSACTIONS ON SOFTWARE ENGINEERING 1988年第10期14卷 1432-1442页

作者： BASTANI, FB YEN, IL CHEN, IR Department of Computer Science University of Houston—University Park Houston TX 77004

Software for industrial process-control systems, such as nuclear power plant safety control systems and robots, can be very complex because of the large number of cases which must be considered. The design approach proposed here uses decentralized control concepts and is based on Dijkstra's concept of self-stabilizing systems. This method greatly simplifies the software, so that its correctness can be verified more easily. We describe a simple control system for a simulated robot which is tolerant of partial failure of controllers and mechanisms, and permits on-line repair and enhancement of the control functions. [ABSTRACT FROM AUTHOR]

关键词： distributed control Index Terms-Correctness proofs inherently fault tolerant programs process-control systems relaxation algorithms resilient software termination/convergence

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ON A CONSISTENCY MEASURE FOR OBJECT LABELING PROBLEMS

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FUZZY SETS AND SYSTEMS 1987年第1期23卷 55-71页

作者： SHVAYTSER, H Department of Computer Science The Hebrew University of Jerusalem 91904 Jerusalem Israel

The problem of defining a consistency measure for object labeling problems is addressed. The optimal probabilistic measures are derived for both discrete and fuzzy solutions. Alternative fuzzy consistency measures are suggested, based on the error each object has in estimating its label using the labels of its neighbors. In general, the best estimation is impractical from computational complexity aspects as well as information considerations. However, if the information available about the problem is probabilities of pairs of events, the best estimation is a linear form.

关键词： Consistency relaxation algorithms Object labeling Fuzzy measures

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DATA-STRUCTURES FOR NETWORK algorithms ON MASSIVELY PARALLEL ARCHITECTURES

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PARALLEL COMPUTING 1992年第9期18卷 1033-1052页

作者： NIELSEN, SS ZENIOS, SA UNIV PENN WHARTON SCH DEPT DECIS SCI PHILADELPHIA PA 19104 USA UNIV CYPRUS DEPT PUBL & BUSINESS ADM NICOSIA CYPRUS

We develop alternative data structures for the representation of network optimization problems on massively parallel SIMD (i.e. Single Instruction Multiple Data) architectures. These data structures are used to implement a primal-dual algorithm for the optimization of a quadratic function subject to network constraints on the Connection Machine CM-2. In particular, two representations of arbitrary, sparse network topologies - a node-wise and an arc-wise representation - are compared with each other in terms of the efficiency with which certain primal-dual algorithms can be executed. Both implementations are also compared with the performance of the same algorithms when applied to dense, bipartite transportation problems. Particular attention is paid to communication efficiency. To this end, the problem of mapping the problem data to the Connection Machine hypercube network is investigated and a pre-computed, optimized, communication scheme is used. The results, collectively, show that very efficient implementations of network algorithms are possible on massively parallel architectures. This statement is true not only in solving dense, bipartite problems, but, even more importantly, in solving problems with arbitrary, sparse network topologies.

关键词： NETWORK algorithms, DATA STRUCTURES CONNECTION MACHINE CM2 IMPLEMENTATION FEATURES SIMD ARCHITECTURE relaxation algorithms

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On the use of a priori information for sparse signal approximations

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2006年第9期54卷 3468-3482页

作者： Escoda, Oscar Divorra Granai, Lorenzo Vandergheynst, Pierre Ecole Polytech Fed Lausanne Signal Proc Inst CH-1015 Lausanne Switzerland

Recent results have underlined the importance of incoherence in redundant dictionaries for a good behavior of decomposition algorithms like matching and basis pursuit. However, appropriate dictionaries for a given application may not be able to meet the incoherence condition. In such a case, decomposition algorithms may completely fail in the retrieval of the sparsest approximation. This paper studies the effect of introducing a priori knowledge when recovering sparse approximations over redundant dictionaries. Theoretical results show how the use of reliable a priori information (which in this paper appears under the form of weights) can improve the performances of standard approaches such as greedy algorithms and relaxation methods. Our results reduce to the classical case when no prior information is available. Examples validate and illustrate our theoretical statements.

关键词： a priori knowledge greedy algorithms redundant dictionaries relaxation algorithms sparse approximations weighted basis pursuit denoising weighted matching pursuit

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Game theory based bidding strategy for prosumers in a distribution system with a retail electricity market

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IET SMART GRID 2018年第3期1卷 104-111页

作者： Liang, Zheming Su, Wencong Univ Michigan Dept Elect & Comp Engn Dearborn MI 48128 USA

Distributed energy resources (DERs) are deployed vastly to reduce carbon emission, improve power quality and maintain the reliability of distribution systems. With the introduction of new players, such as prosumers, which are constructed with DERs, distribution system operators (DSOs) are facing changes in the retail electricity market. Prosumers need a well-defined strategic bidding mechanism to maximize their operation revenue, while DSOs need a new market clearing mechanism for the changed retail electricity market. Thus, an innovative game-theoretic market framework for a prosumer-centric retail electricity market is proposed. A bilevel algorithm is adopted to model new features of DSOs, utility companies and prosumers. The supply function equilibrium model, Nikaido-Isoda functions, and relaxation algorithms are applied to analyse the competition among key participants in a retail electricity market. Extensive simulation results are employed to illustrate and validate the effectiveness of the proposed framework for bidding strategies of prosumers with a retail electricity market. Specifically, the strategy with dumping-bid or abnormal-bid from a prosumer is suppressed by the market operator in the model. Moreover, the sensitivity analysis shows that the proposed framework can handle various numbers of prosumers in the retail electricity market with reasonable computational time and convergence rate.

关键词： power markets game theory retailing distributed power generation distribution system operators market clearing mechanism changed retail electricity market innovative game-theoretic market framework prosumer-centric retail electricity market market operator well-defined strategic bidding mechanism bilevel algorithm supply function equilibrium model relaxation algorithms dumping-bid abnormal-bid sensitivity analysis distributed energy resources B0240E Game theory B8110B Power system management, operation and economics B8120K Distributed power generation

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Finite difference solution of Euler equations arising in variational image segmentation

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NUMERICAL algorithms 1999年第1-4期21卷 353-365页

作者： Spitaleri, RM March, R Arena, D Ist Applicaz Calcolo I-00161 Rome Italy

This paper deals with finite-difference approximations of Euler equations arising in the variational formulation of image segmentation problems. We illustrate how they can be defined by the following steps: (a) definition of the minimization problem for the Mumford-Shah functional (MSf), (b) definition of a sequence of functionals Gamma-convergent to the MSf, and (c) definition and numerical solution of the Euler equations associated to the kth functional of the sequence. We define finite difference approximations of the Euler equations, the related solution algorithms, and we present applications to segmentation problems by using synthetic images. We discuss application results, and we mainly analyze computed discontinuity contours and convergence histories of method executions.

关键词： finite difference approximation Euler equations relaxation algorithms variational image segmentation

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Checking for saddlepoint stability: An easy test

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Computational Economics 1996年第4期9卷 317-330页

作者： Boucekkine, Raouf Le Van, Cuong Departamento de Economía Universidad Carlos III de Madrid Madrid Spain 142 rue du Chevaleret CNRS and CEPREMAP Paris France

In this paper, we present a theoretically founded procedure in order to check for saddlepoint stability of rational expectations models. The proposed device uses some specific perturbed finite time approximations of the models and allows for an explicit theoretical foundation. Numerical evidence are presented to study the feasibility of the procedure regarding to the scales and the spectra of the models. In particular, it is shown how to apply it on nonlinear models in connection with relaxation resolution algorithms. Actually, this paper gives a theoretical basis to the heuristic sensitivity tests traditionally conducted for saddlepoint stability assessment.

关键词： Expectations Saddlepoint paths Terminal conditions Perturbations relaxation algorithms

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