Talk:Line search

The term "linesearch" is used here incorrectly. Linesearch refers to optimization of one dimensional functions f: R->R only.

Not true. Reference :- your favourite optimization text. mat_x 09:23, 21 August 2006 (UTC)

Actually, I believe Sabamo is correct. See e.g. [1], page 147: "one-dimensional unconstrained optimization... [is] usually called line search."

It also seems to me that the spelling "line search" (800,000 Google hits) is much more common than "linesearch" (48,000 Google hits). I think this page should be moved, and also edited extensively. --Zvika 09:13, 2 October 2007 (UTC)

I came here hoping to find line search, a method of optimizing f: R->R and was disapointed to find this page. We need to move it to make room for the correct page. Does anybody know what these algorithms might be called? I am not sure that they are refered to as a class in any textbook. If that is true, then I think the page should be largely deleted. As for a ref. for the claim that it is 1D, "Optimization" by Kenneth Lange (a Springer textbook) refers to line search as a an optimization of f:Rⁿ -> R along a search direction so that you are searching g:R->R where g(d) = f(x+ds), and s is a vector (the search direction). PDBailey (talk) 00:34, 21 April 2009 (UTC)

Rename the article to line search method

• The term One dimensional optimization refers to optimizing a function f:R->R
• Given a function f: R^n -> R and two vectors p and q in R^n, the word line search refers to optimizating of the function function phi(alpha) = f(p+alpha q).
• A Line search method is an algorithm that applies line searches to optimize a function of several variables

Requested move

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the proposal was move the page from "Linesearch" to Line search, per the discussion below. Dekimasuよ! 07:54, 22 October 2007 (UTC)

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Following the discussion above I have entered a formal request for moving the article back to Line search. As I wrote above, the main reason is that the spelling "line search" (800,000 Google hits) is much more common than "linesearch" (48,000 Google hits). --Zvika 18:37, 11 October 2007 (UTC)

Oppose for now. Zvika's Google search is useless trivia unless he can show that a good portion of the hits in either case deal with the particular subject of this article, and unless it is even more overwhelming if it can be whittled down to those which do, I wouldn't find it convincing enough to move from a name getting 48,000 hits in any case; there may well be other factors which would affect our choice under Wikipedia naming conventions. Gene Nygaard 16:31, 13 October 2007 (UTC)

• Here is some hopefully more convincing evidence:
  1. A search for "line search" +optimization yielded 267,000 results, whereas a search for "linesearch" +optimization yielded only 25,000 results. A brief examination of the first 20 results showed they are all indeed about the line search method.
  2. A similar search in scholar resulted in 13,300 results for "line search" +optimization and only 1,120 for "linesearch" +optimization.
  3. As mentioned above, the lecture notes (also available as a printed textbook) of Nemirovski and Ben-Tal use the two-word term.

In summary, obviously the one-word term is also used, but it seems to me that it is much less common. --Zvika 11:39, 14 October 2007 (UTC)

If it's roughly 10:1 across the board, I'd probably support it; if it were more like 3:1 or less, I wouldn't see any compelling reason for a change, because the accuracy of determinations of he usage ratios aren't very precise in any case and redirects would suffice. But if there are distinctions on who is using it each way, that still might not be determinative. Are the differences time-sensitive? Maybe it is an evolution, a trend to change the terminology by the professionals in the field. Maybe something recommended by some professional organization in the field. Or is it location-sensitive? In that case we might have to worry about Wikipedia:Manual of Style#National varieties of English. I'm not strongly opposed to the move, but let's still wait and see if anybody else has any concerns for some reason or another. Gene Nygaard 13:02, 14 October 2007 (UTC)

Along the national varieties of English line, your additional search term fell under that too. Google doesn't give quite the same results if you include "optimisation" rather than "optimization" in your search, but it's still about 10:1. A significant number of them do have hyphens, however, see below. It might be that it is often used as an adjective but with several different possibilities for the noun it is used with, but pretty much the same meaning with various nouns. In that case, its probably used as a stand-alone noun to keep it at just the one-word, two-word, or hyphenated version. Gene Nygaard 13:24, 14 October 2007 (UTC)

I would support a move to line search. FWIW, Numerical Recipes uses the term "line minimization". Jheald 16:05, 15 October 2007 (UTC)

New comment. In this article the term seems to be mostly used as an adjective. That raises two additional concerns:

• Should it include a noun under Wikipedia:Naming conventions#Redirect adjectives to nouns and the rest of those conventions? (And even if that isn't necessary, are there adjective-noun combinations which should redirect here?)
• Do we need to worry about hyphenated or not as well, including "line-search" in the discussion. In any case, that redlink should be fixed. Gene Nygaard 13:12, 14 October 2007 (UTC)

Support move to "line search". Major books on optimization, research reports, and journal papers of my acquaintance use the two word form. For example, the classic text Practical Optimization by Gill, Murray, and Wright (ISBN 978-0-12-283952-8) can be searched at Amazon.com to confirm the phrase "line search". Or try Practical Methods of Optimization by Fletcher (ISBN 978-0-471-49463-8), and Linear and Nonlinear Programming, 2nd ed. by Luenberger (ISBN 978-1-4020-7593-3). --KSmrq^T 22:18, 19 October 2007 (UTC)

The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Exact Line Search

This article seems to put loads of emphasis on the inexact line search, and states that one way of solving this is through the backtracking line search (which is obviously true). However, there is very little explanation of what an exact line search is. You can use the bisection method, for example, but other methods such as Newton or secant work fine as well. The term "exact" might be historically confusing because we use inexact method to get the "exact" solution. Namely, the primary difference between inexact liine searches and exact ones is that the former attempts to lower the objective function (by some amount: i.e. Armijo or Wolfe conditions) while the latter tries to find a value such that the gradient with respect to the function in the direction of the move becomes zero (i.e. if f(x+alpha*p) = g(alpha), then g'(alpha) = del*f(x+alpha*p)^T*p ---> 0 -- therefore the gradient at the position and the step vector,p, are orthogonal to one another. I believe that something like this needs to presented in the main article; unfortunately, I'm too busy at the moment to sort this out. — Preceding unsigned comment added by 2.222.44.210 (talk) 01:02, 5 December 2011 (UTC)

When used for quasi-Newton methods, exact line search is not very useful. Are there other articles that link here? Does anybody care about exact line search? 0¹⁸ (talk) 02:08, 5 December 2011 (UTC)