- Referenced in 610 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 518 articles
- based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian...
- Referenced in 315 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 273 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 134 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 155 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 211 articles
- predictor_corrector algorithm. It is based on Newton steps on the perturbed optimality system...
- Referenced in 194 articles
- solution of the implicit equations by quasi Newton methods. In this paper the authors consider...
- Referenced in 163 articles
- basis factorizations, search directions, line-searches, and Newton iterations. The paper contains performance statistics...
- Referenced in 91 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 110 articles
- TRON is a trust region Newton method for the solution of large bound-constrained optimization...
- Referenced in 106 articles
- inverse Hessian matrix in the Quasi-Newton method in classical optimization. In contrast to most...
- Referenced in 100 articles
- This modification is based on the quasi-Newton BFGS updating formula. The computational scheme...
- Referenced in 56 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 57 articles
- combination of steepest descent and the Gauss-Newton method. When the current solution ... correct solution, it becomes a Gauss-Newton method...
- Referenced in 74 articles
- remarkable relationship of Anderson acceleration to quasi-Newton (secant updating) methods and extended...
- Referenced in 42 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 66 articles
- distributions. The name energy derives from Newton’s gravitational potential energy, and there...
- Referenced in 65 articles
- maximization; the default is a dual quasi-Newton algorithm. Successful convergence of the optimization problem...