- Referenced in 575 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 120 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 477 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 40 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 319 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 173 articles
- basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from...
- Referenced in 126 articles
- Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP (greedy...
- Referenced in 42 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 174 articles
- hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme...
- Referenced in 271 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 31 articles
- extensions of the outer-approximation algorithm for the equality relaxation strategy. The MINLP algorithm inside...
- Referenced in 59 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 100 articles
- developed optimization algorithms based on branch-and-cut and constraint satisfaction, and approximation techniques including...
- Referenced in 56 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 77 articles
- ahead Lanczos algorithm that, by itself, can also be used to obtain approximate eigenvalues ... with Fortran 77 implementations of the QMR algorithm and variants thereof, and of the three ... discuss some of the features of the algorithms in the package, with emphasis ... other for the computation of eigenvalue approximations. We present some numerical examples from applications where...
- Referenced in 50 articles
- routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior...
- Referenced in 22 articles
- iterated eigenvalue algorithm for approximating roots of univariate polynomials. The author studies an iterative algorithm ... that approximates all roots of a univariate polynomial. The iteration is based on floating-point ... conditioned polynomials are carefully implemented for the algorithms...
- Referenced in 26 articles
- Approximate probabilistic model checking. Symbolic model checking methods have been extended recently to the verification ... model checking algorithm. In this paper, we propose an approximation method to verify quantitative properties ... Markov chains. We give a randomized algorithm to approximate the probability that a property expressed ... confidence by a probabilistic system. Our randomized algorithm requires only a succinct representation...
- Referenced in 130 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 39 articles
- constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving ... number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton ... using the preconditioned Conjugate Gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner...