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On Projection Algorithms for Solving Convex Feasibility Problems
, 1996
"... Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of the ..."
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Cited by 142 (24 self)
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Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated . Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given. 1991 M.R. Subject Classification. Primary 47H09, 49M45, 6502, 65J05, 90C25; Secondary 26B25, 41A65, 46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65K05, 90C90, 92C55. Key words and phrases. Angle between two subspaces, averaged mapping, Cimmino's method, computerized tomography, convex feasibility problem, convex function, convex inequalities, convex programming, convex set, Fej'er monotone sequence, firmly nonexpansive mapping, H...
Encapsulating Multiple CommunicationCost Metrics in Partitioning Sparse Rectangular Matrices for Parallel MatrixVector Multiplies
"... This paper addresses the problem of onedimensional partitioning of structurally unsymmetricsquare and rectangular sparse matrices for parallel matrixvector and matrixtransposevector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational load ..."
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Cited by 35 (22 self)
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This paper addresses the problem of onedimensional partitioning of structurally unsymmetricsquare and rectangular sparse matrices for parallel matrixvector and matrixtransposevector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational loads of processors. Most of the existing partitioning models consider only the total message volume hoping that minimizing this communicationcost metric is likely to reduce other metrics. However, the total message latency (startup time) may be more important than the total message volume. Furthermore, the maximum message volume and latency handled by a single processor are also important metrics. We propose a twophase approach that encapsulates all these four communicationcost metrics. The objective in the first phase is to minimize the total message volume while maintainingthe computationalload balance. The objective in the second phase is to encapsulate the remaining three communicationcost metrics. We propose communicationhypergraph and partitioning models for the second phase. We then present several methods for partitioning communication hypergraphs. Experiments on a wide range of test matrices show that the proposed approach yields very effective partitioning results. A parallel implementation on a PC cluster verifies that the theoretical improvements shown by partitioning results hold in practice.
Constraint Programming in Constraint Nets
 Principles and Practice of Constraint Programming: The Newport Papers
, 1993
"... We view constraints as relations and constraint satisfaction as a dynamic process of approaching a stable equilibrium. We have developed an algebraic model of dynamics, called Constraint Nets, to provide a realtime programming semantics and to model and analyze dynamic systems. In this paper, we ex ..."
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Cited by 17 (9 self)
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We view constraints as relations and constraint satisfaction as a dynamic process of approaching a stable equilibrium. We have developed an algebraic model of dynamics, called Constraint Nets, to provide a realtime programming semantics and to model and analyze dynamic systems. In this paper, we explore the relationship between constraint satisfaction and constraint nets by showing how to implement various constraint methods on constraint nets. 1 Motivation Constraints are relations among entities. Constraint satisfaction can be viewed in two different ways. First, in the logical deductive view, a constraint system is a structure hD; `i, where D is a set of constraints and ` is an entailment relation between constraints [20]. In this view, constraint satisfaction is seen as a process involving multiple agents concurrently interacting on the storeasconstraint system by checking entailment and consistency relations and refining the system monotonically. This approach is useful in da...
Parallel Image Restoration Using Surrogate Constraint Methods
, 2006
"... When formulated as a system of linear inequalities, the image restoration problem yields huge, unstructured, sparse matrices even for images of small size. To solve the image restoration problem, we use the surrogate constraint methods that can work efficiently for large problems. Among variants of ..."
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Cited by 6 (2 self)
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When formulated as a system of linear inequalities, the image restoration problem yields huge, unstructured, sparse matrices even for images of small size. To solve the image restoration problem, we use the surrogate constraint methods that can work efficiently for large problems. Among variants of the surrogate constraint method, we consider a basic method performing a single block projection in each step and a coarsegrain parallel version making simultaneous block projections. Using several stateoftheart partitioning strategies and adopting different communication models, we develop competing parallel implementations of the two methods. The implementations are evaluated based on the per iteration performance and on the overall performance. The experimental results on a PC cluster reveal that the proposed parallelization schemes are quite beneficial.
Constraint Programming in Constraint Nets
, 1993
"... We view constraints as relations and constraint satisfaction as a dynamic process of approaching the solution set of the constraints. We have developed a semantic model for dynamic systems, called Constraint Nets, to provide a realtime programming semantics and to model and analyze dynamic systems. ..."
Abstract
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We view constraints as relations and constraint satisfaction as a dynamic process of approaching the solution set of the constraints. We have developed a semantic model for dynamic systems, called Constraint Nets, to provide a realtime programming semantics and to model and analyze dynamic systems. In this paper, we explore the relationship between constraint satisfaction and constraint nets by showing how to implement various constraint methods on constraint nets. In particular, we examine discrete and continuous methods for discrete and continuous domain constraint satisfaction problems. Hard and soft constraints within the framework of unconstrained and constrained optimization are considered. Finally, we present an application of this online constraint satisfaction framework to the design of robot control systems. 1.2 Motivation Constraints are relations among entities. Constraint satisfaction can be viewed in two different ways. In a logical deductive view, a constraint system...