- Referenced in 648 articles
- particular focus on automated solution of differential equations by finite element methods. FEniCS...
- Referenced in 161 articles
- nonconvex, but must be differentiable. A particular attention will be paid to problems with ... stands for Sequential Quadratic Programming, a method invented in the mid-seventies, which ... algorithm requires finding a solution to a quadratic program (QP). This is a simpler optimization ... find an approximate solution with a good precision (this is particularly true when second derivatives...
- Referenced in 320 articles
- guaranteed to produce a nearly optimal solution in a finite number of iterations. We also ... trust region Newton’s method. In particular, we prove that under reasonable assumptions the sequence...
- Referenced in 223 articles
- powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade ... exploiting structure in a polynomial system, in particular its sparsity. In this paper the structure ... features a great variety of root-counting methods among its tools. The outline...
- Referenced in 80 articles
- numerical solution of time dependent partial differential equations, particularly in two or more space dimensions ... using the method of lines. A code based on this algorithm is illustrated by application...
- Referenced in 73 articles
- review other solution approaches and compare the numerical results with our method. We also extend ... particular, for dense graphs, where linear programming-based methods fail, our method performs very well ... Exact solutions are obtained in a reasonable time for any instance of size...
- Referenced in 9 articles
- Wave Scattering, and Eigenvalue Problems Using Particular Solutions and Integral Equations. MPSpack is a user ... MATLAB toolbox that implements the method of particular solutions, nonpolynomial FEM, the method of fundamental...
- Referenced in 109 articles
- generated. In an evolution strategy, new candidate solutions are sampled according to a multivariate normal ... method to update the covariance matrix of this distribution. This is particularly useful ... Quasi-Newton method in classical optimization. In contrast to most classical methods, fewer assumptions ... made. Only the ranking between candidate solutions is exploited for learning the sample distribution...
- Referenced in 127 articles
- round a sequence of fractional solutions of the LP relaxation, until a feasible ... blind) with more clever rounding heuristics. In particular, we investigate the use of a diving ... down the method and with a significantly better quality of the feasible solutions found...
- Referenced in 111 articles
- solution of large bound-constrained optimization problems. TRON uses a gradient projection method to generate ... Cauchy step, a preconditioned conjugate gradient method with an incomplete Cholesky factorization to generate ... step. The use of projected searches, in particular, allows TRON to examine faces...
- Referenced in 25 articles
- ascent methods is particularly well-suited for taking advantage of good initial dual solutions ... cost ﬂow problems. For this reason, these methods are extremely eﬃcient for reoptimization and sensitivity...
- Referenced in 44 articles
- that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties ... particularly Hamiltonian systems. Assuming only basic knowledge of numerical quadrature and Runge-Kutta methods, this ... with an introduction to the line integral methods. It describes numerous Hamiltonian problems encountered ... methods: the energy-conserving Runge-Kutta methods, also known as Hamiltonian boundary value methods (HBVMs...
- Referenced in 105 articles
- introduce a computer program PENNON for the solution of problems of convex nonlinear and semidefinite ... generalized version of the augmented Lagrangian method, originally introduced by Ben-Tal and Zibulevsky ... test examples show that PENNON is particularly suitable for large sparse problems...
- Referenced in 9 articles
- than a numerical or analytical method of solution. In particular, options are retained to reduce ... particular with the various versions of the B2 code. The semi-implicit iterative coupling method...
- Referenced in 15 articles
- different fields. Solution methods exist, but are either especially tailored to very particular classes ... engineering, the interest in general purpose solution methods is growing. The aim of this paper...
- Referenced in 35 articles
- Points The paper discusses methods for the computation of solution paths of a nonlinear system ... particular, for the corrector iteration the Gauss-Newton method is used where the QR-factorization...
- Referenced in 39 articles
- following applications: 1. Formulation and solution of particular optimization problems that are described in Chapter ... specialized optimization routines (or subroutines) based on methods described in Chapter 3. 3. Designing...
- Referenced in 53 articles
- implements a NURBS-based Galerkin finite element method (FEM), popularly known as isogeometric analysis ... data structures for the solution of scientific problems, particularly those modeled by partial differential equations...
- Referenced in 61 articles
- multivariate) normal random effects or factors. Two methods are available for numerical integration: Quadrature ... quadrature points has been used by comparing solutions with different numbers quadrature points. In most ... perform better than ordinary quadrature. This is particularly the case if the cluster sizes...
- Referenced in 20 articles
- method. The final solution is globally optimal with respect to energy functions. In particular...