1,721,056 research outputs found
On the application of multiple-deme parallel genetic algorithms in astrophysics
No full textWe present a Parallel Genetic Algorithm (PGA) for the solution of a constrained global optimization problem arising in the detection of gravitational waves through the matched filter technique. This is a hard problem, since it has a black-box stochastic objective function, which is highly nonlinear, multiextremal and computationally expensive. Our PGA uses multiple subpopulations (demes) that evolve separately by the application of genetic operators tailored to the optimization problem; individuals are exchanged from time to time through a suitable migration mechanism. Numerical experiments performed on a set of representative test problems show that the PGA is able to solve the problem with the same accuracy and reliability as the grid search, which is the reference algorithm for this problem, but requiring a smaller execution time
P2GP - Proportionality-based 2-phase Gradient Projection method
No full textP2GP is a MATLAB code for the solution of Quadratic Programming problems with a Single Linear constraint and Bounds on the variables (SLBQPs). The problems are not required to be strictly convex. The code implements the Proportionality-based 2-phase Gradient Projection method proposed in
D. di Serafino, G. Toraldo, M. Viola, J. Barlow, A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables, SIAM Journal on Optimization, 28 (4), pp. 2809-2838, ISSN: 1052-6234, doi: 10.1137/17M1128538.
It also includes SLBQPgen, a generator of SLBQPs (and BQPs), described in Section 5.1 of the aforementioned article
A Parallel Implementation of a Multigrid Multiblock Euler Solver on Distributed Memory Machines
No full textThis paper presents a parallel Multigrid solver for the computation of steady compressible inviscid flows around 2D and 3D aerodynamic configurations, on MIMD distributed memory machines. It is a parallel version of a large CFD code, ZEN Flow Solver, developed by the Italian Aerospace Research Center (CIRA). The sequential solver uses a multiblock structured grid and a cell-centered finite volume scheme, and implements an explicit time-marching procedure, based on a Full Multigrid algorithm. The parallel version has been developed using a domain decomposition technique, based on the multiblock structure of the grid. Moreover, a convergence criterion has been introduced in the Multigrid algorithm. The parallel solver has been implemented using the PVM communication environment. Experiments have been carried out using a Convex Meta Series, a cluster of HP PA-RISC workstations. Numerical results and parallel efficiency concerning a 2D and a 3D test case are analysed here. © 1997 Elsevier Science B.V
A matrix-free approach to build band preconditioners for large-scale bound-constrained optimization
No full textWe propose a procedure for building symmetric positive definite band preconditioners for large-scale symmetric, possibly indefinite, linear systems, when the coefficient matrix is not explicitly available, but matrix-vector products involving it can be computed. We focus on linear systems arising in Newton-type iterations within matrix-free versions of projected methods for bound-constrained nonlinear optimization. In this case, the structure and the size of the matrix may significantly change in subsequent iterations, and preconditioner updating algorithms that exploit information from previous steps cannot be easily applied. Our procedure is based on a recursive approach that incrementally improves the quality of the preconditioner, while requiring a modest number of matrix-vector products. A strategy for dynamically choosing the bandwidth of the preconditioners is also presented. Numerical results are provided, showing the performance of our preconditioning technique within a trust-region Newton method for bound-constrained optimization
A matrix-free approach to build band preconditioners for large-scale bound-constrained optimization
No full textWe propose a procedure for building symmetric positive definite band preconditioners for large-scale symmetric, possibly indefinite, linear systems, when the coefficient matrix is not explicitly available, but matrix-vector products involving it can be computed. We focus on linear systems arising in Newton-type iterations within matrix-free versions of projected methods for bound-constrained nonlinear optimization. In this case, the structure and the size of the matrix may significantly change in subsequent iterations, and preconditioner updating algorithms that exploit information from previous steps cannot be easily applied. Our procedure is based on a recursive approach that incrementally improves the quality of the preconditioner, while requiring a modest number of matrix-vector products. A strategy for dynamically choosing the bandwidth of the preconditioners is also presented. Numerical results are provided, showing the performance of our preconditioning technique within a trust-region Newton method for bound-constrained optimization
Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems
Full text linkAlgebraic multilevel preconditioners for algebraic problems arising from the discretization of a class of systems of coupled elliptic partial differential equations (PDEs) are presented. These preconditioners are based on modifications of Schwarz methods and of the smoothed aggregation technique, where the coarsening strategy and the restriction and prolongation operators are defined using a point-based approach with a primary matrix corresponding to a single PDE. The preconditioners are implemented in a parallel computing framework and are tested on two representative PDE systems. The results of the numerical experiments show the effectiveness and the scalability of the proposed methods. A convergence theory for the twolevel case is presented
Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems
No full textWe consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semidefinite on an appropriate subspace, Dollar et al. [SIAM J. Matrix Anal. Appl., 28 (2006), pp. 170-189] describe how to apply the conjugate gradient (CG) method coupled with a constraint preconditioner, a choice that has proved to be effective in optimization applications. We investigate the design of constraint-preconditioned variants of other Krylov methods for regularized systems by focusing on the underlying basis-generation process. We build upon principles laid out by Gould, Orban, and Rees [SIAM J. Matrix Anal. Appl., 35 (2014), pp. 1329-1343] to provide general guidelines that allow us to specialize any Krylov method to regularized saddle-point systems. In particular, we obtain constraint-preconditioned variants of Lanczos and Arnoldi-based methods, including the Lanczos version of CG, MINRES, SYMMLQ, GMRES(), and DQGMRES. We also provide MATLAB implementations in hopes that they are useful as a basis for the development of more sophisticated software. Finally, we illustrate the numerical behavior of constraint-preconditioned Krylov solvers using symmetric and nonsymmetric systems arising from constrained optimization
- …
