Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations)

[Robbie Morrison]

Hello Andrew

I sub-edited your KKT suggestion and is now here:

  http://en.wikibooks.org/wiki/Talk:GLPK/Solution_information#.232

Please feel free to revise it, best wishes, Robbie

------------------------------------------------------------
To:          Robbie Morrison <address@hidden>
Subject:     Re: optimality conditions paragraph (KKT and LP formulations)
Message-ID: <address@hidden>
From:        Andrew Makhorin <address@hidden>
Date:        Wed, 11 May 2011 11:37:42 +0400
------------------------------------------------------------

> Hi Robbie,
>
>> In reference to the following [help-glpk] thread and
>> GLPK wikibook page:
>>
>>   GLPK wikibook : newish solution information page
>>   http://lists.gnu.org/archive/html/help-glpk/2011-05/msg00022.html
>>   http://en.wikibooks.org/wiki/GLPK/Solution_information
>>
>> I drafted a paragraph on optimality conditions which
>> is sitting on the associated wikibook discussion page:
>>
>>   http://en.wikibooks.org/wiki/Talk:GLPK/Solution_information
>>
>> Please add comments and/or make changes there.  I will
>> transfer this text over to the main page in a week or so.
>>
>
> I attempted to rewrite the very first paragraph. But I think that a
> reference to appropriate textbook would be better.
>
>     In general case of non-linear programming (NLP) problem the
>     Karush-Kuhn-Tucker optimality conditions (KKT) are necessary
>     conditions of the first order for a solution to be (locally)
>     optimal (together with some regularity conditions that also have
>     to be satisfied). Linear programming (LP) problem is a
>     particular case of NLP, where the feasible region and the
>     objective function are convex, and in this particular case the
>     KKT conditions are necessary and sufficient conditions for a
>     solution to be globally optimal. The KKT conditions can be
>     applied to basic as well as interior-point solutions of any LP
>     problem. Note, however, that the KKT conditions cannot be
>     applied to solutions of mixed-integer linear programming (MIP)
>     problems.
>
> Best regards,
>
> Andrew Makhorin

---
Robbie Morrison
PhD student -- policy-oriented energy system simulation
Technical University of Berlin (TU-Berlin), Germany
University email (redirected) : address@hidden
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