124,599 research outputs found
Lagrangean decomposition for large-scale two-stage stochastic mixed 0-1 problems
In this paper we study solution methods for solving the dual problem corresponding to the Lagrangean Decomposition of two stage stochastic mixed 0-1 models. We represent the two stage stochastic mixed 0-1 problem by a splitting variable representation of the deterministic equivalent model, where 0-1 and continuous variables appear at any stage. Lagrangean Decomposition is proposed for satisfying both the integrality constraints for the 0-1 variables and the non-anticipativity constraints. We compare the performance of four iterative algorithms based on dual Lagrangean Decomposition schemes, as the Subgradient method, the Volume algorithm, the Progressive Hedging algorithm and the Dynamic Constrained Cutting Plane scheme. We test the conditions and properties of convergence for medium and large-scale dimension stochastic problems. Computational results are reported.Progressive Hedging algorithm, volume algorithm, Lagrangean decomposition, subgradient method
Distributed Large Scale Network Utility Maximization
Recent work by Zymnis et al. proposes an efficient primal-dual interior-point
method, using a truncated Newton method, for solving the network utility
maximization (NUM) problem. This method has shown superior performance relative
to the traditional dual-decomposition approach. Other recent work by Bickson et
al. shows how to compute efficiently and distributively the Newton step, which
is the main computational bottleneck of the Newton method, utilizing the
Gaussian belief propagation algorithm.
In the current work, we combine both approaches to create an efficient
distributed algorithm for solving the NUM problem. Unlike the work of Zymnis,
which uses a centralized approach, our new algorithm is easily distributed.
Using an empirical evaluation we show that our new method outperforms previous
approaches, including the truncated Newton method and dual-decomposition
methods. As an additional contribution, this is the first work that evaluates
the performance of the Gaussian belief propagation algorithm vs. the
preconditioned conjugate gradient method, for a large scale problem.Comment: In the International Symposium on Information Theory (ISIT) 200
Self-Dual Conformal Supergravity and the Hamiltonian Formulation
In terms of Dirac matrices the self-dual and anti-self-dual decomposition of
a conformal supergravity is given and a self-dual conformal supergravity theory
is developed as a connection dynamic theory in which the basic dynamic variabes
include the self-dual spin connection i.e. the Ashtekar connection rather than
the triad. The Hamiltonian formulation and the constraints are obtained by
using the Dirac-Bergmann algorithm.
PACS numbers: 04.20.Cv, 04.20.Fy,04.65.+
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