Showing papers by "Aharon Ben-Tal published in 1990"
TL;DR: In this paper, an explicit determinantal formula for the least square solution of an over-determined system of linear equations was derived, and it was shown that the least squares solution lies in the convex hull of the solutions to the square subsystems of the original system.
49 citations
TL;DR: Curved Searchalgorithm as discussed by the authors is a family of algorithms for unconstrained minimization of an n-variable twice continuously differentiate function /. Unlike classical met hods, which improve a current solution by moving along a straight line, the new methods improve the solution by move along a quadratic curve in R n.
Abstract: The paper introduces a family of algorithms for unconstrained minimization of an nvariable twice continuously differentiate function /. Unlike classical met hods, which improve a current solution by moving along a straight line, the new methods improve the solution by moving along a quadratic curve in R nThe specific curve is determined by minimizing an appropriate model of f The algorithms thus obtained (called Curved Searchalgorithms) all possess a global convergence property combined with a quadratic rate of convergence. They are all using the same information and employing the same computational effort as the Newton method, which is in fact a member of this class, versions of cured search methods with inexact line search of the Goldstein-type are studied as well, retaining the above desirable convergence properties. We also discuss a version, called β-method not requiring a line search altogether. Computational experience reported in the paper points out to the potential improvement, which may be gain...
23 citations