What is the Armijo rule?

The Armijo Rule is an example of a line search: Search on a ray from xk in direction of locally decreasing f . Armijo procedure is to start with m = 0 then increment m until sufficient decrease is achieved, i.e., λ = βm = 1,β,β2,… This approach is also called “backtracking” or performing “pullbacks”.

What is inexact line search?

Line search method can be categorized into exact and inexact methods. The exact method, as in the name, aims to find the exact minimizer at each iteration; while the inexact method computes step lengths to satisfy conditions including Wolfe and Goldstein conditions.

What is meant by a line search?

Reconnaissance along a specific line of communications, such as a road, railway or waterway, to detect fleeting targets and activities in general.

What are different line search strategies?

The major algorithms available are the steepest descent method, the Newton method, and the quasi-Newton methods. These algorithms are explained in more depth elsewhere within this Wiki. When using these algorithms for line searching, it is important to know their weaknessess.

What is line search gradient descent?

The line search approach first finds a descent direction along which the objective function will be reduced and then computes a step size that determines how far. should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method.

Why do we need a line search in gradient descent approaches?

Gradient descent, although computationally efficient, provides a slow rate of convergence. This is where line search comes into place and provides much better rate of convergence at a slight increase in computational spending.

Why do we need line search?

If the step size is too small, it can take forever to converge and if it is too big, we might overshoot the minima and oscillate back and forth. Line search is a strategy for picking a good value of step size which results in a quicker convergence.

What is direction search method?

The search direction is modified from the steepest descent direction such that the centrality conditions can be approached iteratively while maintaining a descent direction of the objective function. We are able to achieve a local minimum by traversing the interior of the feasible domain.