Talk:Interior-point method

These algorithms have been inspired by Karmarkar's algorithm, developed by Narendra Karmarkar in 1984 for linear programming. The basic elements of the method consists of a self-concordant barrier function used to encode the convex set. Contrary to the simplex method, it reaches the optimal vertex by traversing the interior of the feasible region. This seems a bit complex - I'm not sure if it's helped me understand what an interior point method is, why I'd use it or what I'd be doing. I'm going to traverse the interior of a convex set - right? Is this method really this complex? Has anyone got a source that is as simple as Shewchuk's "Introduction to the Conjugate Gradient Method without the Agonising Pain"? --Dilaudid (talk) 11:23, 27 November 2007 (UTC)[reply]

Try the book of S. Wright given in the literature. At least the intoduction.195.128.250.6 (talk) 22:07, 8 October 2008 (UTC)[reply]

"Yurii Nesterov and Arkadii Nemirovskii came up with a special class of such barriers that can be used to encode any convex set." When did they do this? Was it before or after Karmarkar? What is the citation? Duoduoduo (talk) 16:20, 25 January 2010 (UTC)[reply]

in 1994, after Karmarkar. Ref to original N&N paper in the overview which I've added Serg3d2 (talk) 07:57, 21 February 2011 (UTC)[reply]

I opt for revising the text for grammar, it is sometimes difficult to understand the text when many articles are missing and when sentences are simply incomplete (especially the Section "Primal-dual interior point method for nonlinear optimization"). -- 09:00, 22 March 2011 (UTC) —Preceding unsigned comment added by 128.130.71.144 (talk)

Expanding article for other IPM applications

IPM for constrained nonlinear optimization exampled in article is the most simple IPM technically. Should other applications - LP, sequential quadratic etc. also explained in details? I had experience only with IPM for constrained nonlinear, by simple retelling or copy/pasting I can miss some niceties in those other applications of IPM.Serg3d2 (talk) 06:18, 27 February 2011 (UTC)[reply]

Another question - should symmetric IPM modification be explaned here, or it's too not-notable/trivial?Serg3d2 (talk) 06:29, 27 February 2011 (UTC)[reply]

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Ungrammatical and/or incomplete sentence not containing a statement

In the current version of the article I read: "An interior point method, discovered by Soviet mathematician I. I. Dikin in 1967 and reinvented in the U.S. in the mid-1980s.". This sentence is ungrammatical and/or incomplete and contains no statement. Could the author indicate what s/he meant to say?Redav (talk) 10:59, 26 April 2020 (UTC)[reply]

You say quadratic, isnt it linear?

The text describes d^t x subject to x^t A x .... constraint as quadratic with quadratic constraint, but isnt this linear with quadratic constraint? Indeed, if you mouse over the heading you get the correct formulation for QCQP, which is not d^t x.

There's related point earlier in the text, which says "without loss of generality we can assume the objective function is linear". That is a bit too much of a sweeping statement for my taste. Microsiliconinc (talk) 13:18, 4 February 2024 (UTC)[reply]