The Convergence of Single - Rank Quasi - Newton Methods
نویسندگان
چکیده
Analyses of the convergence properties of general quasi-Newton methods are presented, particular attention being paid to how the approximate solutions and the iteration matrices approach their final values. It is further shown that when Broyden's algorithm is applied to linear systems, the error norms are majorised by a superlinearly convergent sequence of an unusual kind.
منابع مشابه
A Note on Pan’s Second-order Quasi-newton Updates
This note, attempts to further Pan’s second-order quasi-Newton methods([1]). To complement the numerical implementation, the linear convergence of a rank-one second-order update and the least change property are presented.
متن کاملQuasi-Newton Methods for Nonconvex Constrained Multiobjective Optimization
Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.
متن کاملConvergence of quasi-Newton matrices generated by the symmetric rank one update
Quasi-Newton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paper gives conditions under which these approximations can be proved to converge globally to the true Hessian matrix, in the case where the Symmetric Rank One update formula is used. The rate of convergence ...
متن کاملOn the Behavior of Damped Quasi-Newton Methods for Unconstrained Optimization
We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...
متن کاملAdaptive Fista
In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA), however we locally optimize the extrapolation parameter by carrying out an exact (or inexact) line search. It turns out that in some situations, the proposed algorithm is equivalent to a class of SR1 (identity minus rank 1) proximal quas...
متن کامل