We consider (relaxed) additive and multiplicative iterative space decomposition methods for the minimization of sufficiently smooth functionals without constraints. We develop a general framework which unites existing...
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We consider (relaxed) additive and multiplicative iterative space decomposition methods for the minimization of sufficiently smooth functionals without constraints. We develop a general framework which unites existing approaches from both parallel optimization and finite elements. Specifically this work unifies earlier research on the parallel variable distribution method in minimization, space decomposition methods for convex functionals, algebraic Schwarz methods for linear systems and splitting methods for linear least squares. We develop a general convergence theory within this framework, which provides several new results as well as including known convergence results. (C) 1999 Elsevier Science B.V. All rights reserved. MSC: 65H10.
In this paper, a parallel SSLE algorithm is proposed for solving large scale constrained optimization with block-separable structure. At each iteration, the PVD sub-problems are solved inexactly by the SSLE algorithm,...
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In this paper, a parallel SSLE algorithm is proposed for solving large scale constrained optimization with block-separable structure. At each iteration, the PVD sub-problems are solved inexactly by the SSLE algorithm, which successfully overcomes the constraint inconsistency exited in most SQP-type algorithm, and decreases the computation amount as well. Without assuming the convexity of the constraints, the algorithm is proved to be globally convergent to a KKT point of the original problem. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.
A parallel optimization algorithm implemented in a distributed computing environment was applied to nonlinear engineering problems. We deal with the parallel variable distribution (PVD) algorithm, discussing how to ha...
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A parallel optimization algorithm implemented in a distributed computing environment was applied to nonlinear engineering problems. We deal with the parallel variable distribution (PVD) algorithm, discussing how to handle nonlinear constraints and proposing a new domain-partitioning heuristics. The quality of the proposal was first assessed by analyzing its performance for several small nonlinear models associated with classical engineering problems. Then, the parallel distributed code was employed to solve the rigorous model of an existing expander plant, whose constraint-evaluation stage was more complex. Satisfactory speed-up and efficiency values were achieved.
The constraint-partitioning approach achieves a significant reduction in solution time while resolving some large-scale mixed-integer optimization problems. Its theoretical foundation, extended saddle-point theory, wh...
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ISBN:
(纸本)9783642163357
The constraint-partitioning approach achieves a significant reduction in solution time while resolving some large-scale mixed-integer optimization problems. Its theoretical foundation, extended saddle-point theory, which implies the original problem can be decomposed into several subproblems of relatively smaller scale in virtue of the separability of extended saddle-point conditions, still needs to be deliberated carefully. Enlightened by such a plausible theory, we have developed a novel parallel algorithm for convex programming. Our approach not only works well theoretically, but also may be promising in numerical experiments. As the theoretical essence of Support Vector Machine (SVM) is a quadratic programming, we are inspired to apply this new method onto large-scale SVMs to achieve some numerical improvements.
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