Search results for " optimization"
showing 10 items of 2367 documents
Chebyshev’s Method on Projective Fluids
2020
We demonstrate the acceleration potential of the Chebyshev semi-iterative approach for fluid simulations in Projective Dynamics. The Chebyshev approach has been successfully tested for deformable bodies, where the dynamical system behaves relatively linearly, even though Projective Dynamics, in general, is fundamentally nonlinear. The results for more complex constraints, like fluids, with a particular nonlinear dynamical system, remained unknown so far. We follow a method describing particle-based fluids in Projective Dynamics while replacing the Conjugate Gradient solver with Chebyshev’s method. Our results show that Chebyshev’s method can be successfully applied to fluids and potentially…
Decentralized unscented Kalman filter based on a consensus algorithm for multi-area dynamic state estimation in power systems
2015
Abstract A decentralized unscented Kalman filter (UKF) method based on a consensus algorithm for multi-area power system dynamic state estimation is presented in this paper. The overall system is split into a certain number of non-overlapping areas. Firstly, each area executes its own dynamic state estimation based on local measurements by using the UKF. Next, the consensus algorithm is required to perform only local communications between neighboring areas to diffuse local state information. Finally, according to the global state information obtained by the consensus algorithm, the UKF is run again for each area. Its performance is compared with the distributed UKF without consensus algori…
A greedy perturbation approach to accelerating consensus algorithms and reducing its power consumption
2011
The average consensus is part of a family of algorithms that are able to compute global statistics by only using local data. This capability makes these algorithms interesting for applications in which these distributed philosophy is necessary. However, its iterative nature usually leads to a large power consumption due to the repetitive communications among the iterations. This drawback highlights the necessity of minimizing the power consumption until consensus is reached. In this work, we propose a greedy approach to perturbing the connectivity graph, in order to improve the convergence time of the consensus algorithm while keeping bounded the power consumption per iteration step. These …
Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions
2019
We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a natural geometric condition.
Numerical decomposition of geometric constraints
2005
Geometric constraint solving is a key issue in CAD/CAM. Since Owen's seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of inci…
Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems
1994
In this paper, we present several constraint qualifications, and we show that these conditions guarantee the nonvacuity and the boundedness of the Lagrange multiplier sets for general nondifferentiable programming problems. The relationships with various constraint qualifications are investigated.
An optimality test for semi-infinite linear programming
1992
In this paper we present a test to characterize the optimal solutions for the continuous semi-infinite linear programming problem. This optimality characterization is a condition of Kuhn–Tucker type. The resolution of a linear program permits to check the optimality of a feasible point,to detect the unboundedness of the problem and to find descent directions. We give some illustrative examples. We show that the local Mangasarian–Fromovitz constraint qualification is almost equivalent to Slater qualification for this problem. Furthermore, it follows from our study that this optimality condition is always necessary for a wide class of semi-infinite linear programming problems
Exact and Approximate Algorithms for Two–Criteria Topological Design Problem of WAN with Budget and Delay Constraints
2004
This paper studies the problem of designing wide area networks (WAN). In the paper the two-criteria topology assignment problem with two constraints is considered. The goal is select flow routes, channel capacities and network topology in order to minimize the total average delay per packet and the leasing cost of channels subject to the budget constraint and delay constraint. The problem is NP-complete. Then, the branch and bound method is used to construct the exact algorithm. Also the approximate algorithm is presented. Some computational results are reported. Based on computational experiments, several properties of the considered problem are formulated.
The Two-Criteria Topological Design Problem in WAN with Delay Constraint: An Algorithm and Computational Results
2003
The problem is concerned with designing of wide area networks (WAN). The problem consists in selection of flow routes, channel capacities and wide area network topology in order to minimize the total average delay per packet and the leasing cost of channels subject to delay constraint. The problem is NP complete. Then, the branch and bound method is used to construct the exact algorithm. Lower bound of the criterion function is proposed. Computational results are reported. Based on computational experiments, several properties of the considered problem are formulated.
New Geometric Constraint Solving Formulation: Application to the 3D Pentahedron
2014
Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be …