TOPICS
Search

Line Search


A line search is an optimization procedure that chooses a step length along a specified search direction. Given a current point x_k, a direction p_k, and an objective function f, it seeks a scalar alpha_k>0 for which

 x_(k+1)=x_k+alpha_kp_k

produces sufficient improvement. An exact line search minimizes f(x_k+alphap_k) over the allowed values of alpha, while an inexact line search commonly enforces the Armijo or Wolfe conditions.


See also

Method of Steepest Descent, Newton's Method, Optimization Theory

Explore with Wolfram|Alpha

References

Nocedal, J. and Wright, S. J. Numerical Optimization, 2nd ed. New York: Springer, pp. 30-65, 2006.

Cite this as:

Weisstein, Eric W. "Line Search." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LineSearch.html

Subject classifications