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Local Analysis of Inexact Quasi-Newton Methods
Quasi-Newton methods are well known iterative methods for solving nonlinear problems. At each stage, a system of linear equations has to be solved. However, for large scale problems, solving the linear system of equations ...
On the Successive Projections Approach to Least-Squares Problems
In this paper, we suggest a generalized Gauss-Seidel approach to sparse linear and nonlinear least-squares problems. The algorithm, closely related to one given by Elfving (1980), uses the work of Curtis, Powell, and Reid ...
Local and Superlinear Convergence for Truncated Projections Methods
Least change secant updates can be obtained as the limit of iterated projections based on other secant updates. We show that these iterated projections can be terminated or truncated after any positive number of iterations ...
A Convergence Theory for a Class of Quasi-Newton Methods for Constrained Optimization
In this paper we develop a general convergence theory for a class of quasi-Newton methods for equality constrained optimization. The theory is set in the framework of the diagonalized multiplier method defined by Tapia ...
Damped Inexact Quasi-Newton Methods
The inexact quasi-Newton methods are very attractive methods for large scale optimization since they require only an approximate solution of the linear system of equations for each iteration. To achieve global convergence ...