- Referenced in 592 articles
- Chapter 2 studies the local convergence of Newton’s method, inexact Newton methods ... Gauss-Newton method for the solution of nonlinear least squares problems. Both, overdetermined and underdetermined ... implementation details are discussed. Other quasi-Newton methods are sketched. The last chapter...
- Referenced in 495 articles
- based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian...
- Referenced in 305 articles
- this algorithm in a trust region Newton’s method. In particular, we prove that under ... reasonable assumptions the sequence generated by Newton’s method has a limit point which satisfies...
- Referenced in 304 articles
- automatic differentiation and code list generation, interval Newton method, and a short glance ... branch and bound, infeasibility test, interval Newton algorithm applied to the John conditions and computationally...
- Referenced in 263 articles
- NewtonLib. Software repository for Peter Deuflhards Book ”Newton Methods for Nonlinear Problems -- Affine Invariance ... monograph presents a scheme to construct adaptive Newton-type algorithms in close connection with...
- Referenced in 126 articles
- Newton-type minimization via the Lanczos method This paper discusses the use of the linear ... exploited to define a modified Newton method which can be applied to problems that ... problem. The idea of a truncated Newton method is to terminate the iterations earlier ... preconditioned truncated Newton method is described that defines a search direction which interpolates between...
- Referenced in 145 articles
- seventies, which can be viewed as the Newton approach applied to the optimality conditions ... nonconvex. On the other hand, as a Newton method, the SQP algorithm converges very rapidly...
- Referenced in 198 articles
- predictor_corrector algorithm. It is based on Newton steps on the perturbed optimality system...
- Referenced in 191 articles
- solution of the implicit equations by quasi Newton methods. In this paper the authors consider...
- Referenced in 162 articles
- basis factorizations, search directions, line-searches, and Newton iterations. The paper contains performance statistics...
- Referenced in 88 articles
- introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems ... framework is an inexact Newton method globalized by backtracking. Trial steps are obtained using...
- Referenced in 108 articles
- TRON is a trust region Newton method for the solution of large bound-constrained optimization...
- Referenced in 100 articles
- inverse Hessian matrix in the Quasi-Newton method in classical optimization. In contrast to most...
- Referenced in 98 articles
- This modification is based on the quasi-Newton BFGS updating formula. The computational scheme...
- Referenced in 52 articles
- nonstiff systems, and various versions of Newton iteration. In the cases of a direct linear ... solver (dense or banded), the Newton iteration is a Modified Newton iteration, in that ... linear solver, the iteration is an Inexact Newton iteration, using the current Jacobian (through matrix...
- Referenced in 52 articles
- combination of steepest descent and the Gauss-Newton method. When the current solution ... correct solution, it becomes a Gauss-Newton method...
- Referenced in 39 articles
- multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited ... involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions ... Newton equations. Truncation is accomplished in the present version by using the preconditioned Conjugate Gradient ... algorithm (PCG) to solve approximately the Newton equations. The preconditioner M is factored...
- Referenced in 59 articles
- Smooth Support Vector Machine (SSVM). A fast Newton-Armijo algorithm for solving the SSVM converges...
- Referenced in 58 articles
- model reduction methods and modifications of the Newton method for the solution of large Riccati...
- Referenced in 56 articles
- remarkable relationship of Anderson acceleration to quasi-Newton (secant updating) methods and extended...