- Referenced in 185 articles
- deep learning algorithm for solving partial differential equations. High-dimensional PDEs have been a longstanding ... propose to solve high-dimensional PDEs by approximating the solution with a deep neural network ... operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since meshes ... Burgers’ equation. The deep learning algorithm approximates the general solution to the Burgers’ equation...
- Referenced in 643 articles
- complete generality and confine our scope to algorithms that are easy to implement ... into two parts. The first part, occupying approximately 100 pages, is devoted to the optimization ... second part of the book, which is approximately 50 pages long, deals with the optimization ... used to demonstrate the behavior of optimization algorithms. Chapter 7 introduces implicit filtering, a technique...
- Referenced in 151 articles
- highly effective. Even though the algorithm is approximate, optimal solutions are produced with an impressively ... nontrivial instance solved to optimality). Furthermore, the algorithm has improved the best known solutions...
- Referenced in 556 articles
- gradients are sparse. We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit ... Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT...
- Referenced in 45 articles
- performance of several semidefinite programming based approximation algorithms. Using outward rotations, we obtain an approximation ... Williamson. We also obtain an improved approximation algorithm for MAX NAE-f3g-SAT. Finally ... also be used to obtain improved approximation algorithms ... used semidefinite programming to obtain an approximation algorithm...
- Referenced in 402 articles
- Algorithms Library (CGAL), offers data structures and algorithms like triangulations (2D constrained triangulations and Delaunay ... properties, and approximation of ridges and umbilics), alpha shapes, convex hull algorithms...
- Referenced in 231 articles
- basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from...
- Referenced in 255 articles
- spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze ... allows the reader to easily implement the algorithms illustrated throughout the text. The book will...
- Referenced in 46 articles
- rational approximation. We introduce a new algorithm for approximation by rational functions on a real ... Even on a disk or interval the algorithm may outperform existing methods, and on more ... ideas are (1) representation of the rational approximant in barycentric form with interpolation at certain ... based on (1). We present the core algorithm with a Matlab code and nine applications...
- Referenced in 260 articles
- Algorithm 596: Methods for solving systems of nonlinear equations. Chapter 7: Parametrized systems of equations ... equations approach, the code PITCON and simplicial approximation of manifolds are contained. (netlib contin...
- Referenced in 133 articles
- Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP (greedy...
- Referenced in 412 articles
- integer constraints. The idea of the EGO algorithm is to first fit a response surface ... minimum of the surface and improving the approximation by sampling where the prediction error...
- Referenced in 51 articles
- algorithm for computing polynomial zeros, based on Aberth’s method, is presented. The starting approximations ... rounding error analysis, guarantees that the computed approximations are the exact zeros of a “nearby ... This implies the backward stability of our algorithm. We provide a Fortran 77 implementation ... Fortran 77 implementation of our algorithm computed approximations to all the zeros within the relative...
- Referenced in 214 articles
- hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme...
- Referenced in 38 articles
- extensions of the outer-approximation algorithm for the equality relaxation strategy. The MINLP algorithm inside...
- Referenced in 75 articles
- Hybrid Systems. We present a scalable reachability algorithm for hybrid systems with piecewise affine ... compute an over-approximation of the reachable states. The algorithm improves over previous work ... improved approximation model, which drastically improves the accuracy of the algorithm. The algorithm is implemented...
- Referenced in 69 articles
- UOBYQA: unconstrained optimization by quadratic approximation. A new algorithm for general unconstrained optimization calculations ... adjustment of trust region radii. par The algorithm works with the Lagrange functions ... estimate of the error of the quadratic approximation of the function being minimized...
- Referenced in 109 articles
- developed optimization algorithms based on branch-and-cut and constraint satisfaction, and approximation techniques including...
- Referenced in 181 articles
- hand, as a Newton method, the SQP algorithm converges very rapidly, meaning that it requires ... iterations (hence QP solves) to find an approximate solution with a good precision (this ... Therefore, one can say that the SQP algorithm is an appropriate approach when the evaluation...
- Referenced in 61 articles
- routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior...