Line search methods
Author names: Elizabeth Conger
Steward: Dajun Yue and Fengqi You
An algorithm is a line search method if it seeks the minimum of a defined nonlinear function by selecting a reasonable direction vector that, when computed iteratively with a reasonable step size, will provide a function value closer to the absolute minimum of the function. Varying these will change the "tightness" of the optimization. For example, given the function , an initial is chosen. To find a lower value of , the value of is increased by the following iteration scheme
in which is a positive scalar known as the step length and defines the step direction.
Steepest Descent Method
1. Sun, W. & Yuan, Y-X. (2006) Optimization Theory and Methods: Nonlinear Programming (Springer US) p 688.
2. Anonymous (2014) Line Search. (Wikipedia). http://en.wikipedia.org/wiki/Line_search.
3. Nocedal, J. & Wright, S. (2006) Numerical Optimization (Springer-Verlag New York, New York) 2 Ed p 664.