Re: [Help-glpk] GLPK wikibook : newish solution information page

[Meketon, Marc]

In most linear programming textbooks, the optimality conditions are refered to 
differently.  They either use "weak duality" or "complementary slackness" when 
refering to the optimality conditions:

(1) weak duality is when there is a primal feasible solution, a dual feasible 
solution, and the primal objective value equals to the dual objective value

(2) complementary slackness is where there is a primal feasible solution (x), a 
dual feasible solution (y), and whenever x_i is strictly between it's lower and 
upper bounds, the corresponding reduced cost as calculated with  y  is zero.

Both these conditions are equivalent to the KKT, and in the linear programming 
case are fairly trivial to prove.  But the textbooks don't usually call them 
KKT so I believe the wiki page entry should refer it as "Tests for Optimality" 
and then discuss the more precise calculations.

I wish I had some time to write it up more... but I'm behind on doing some 
testing for Xypron and not sure when I'll get that finished.  Maybe someone 
else can?

-Marc

-----Original Message-----
From: address@hidden [mailto:address@hidden On Behalf Of Robbie Morrison
Sent: Thursday, May 05, 2011 11:43 AM
To: GLPK help
Subject: [Help-glpk] GLPK wikibook : newish solution information page


Hi all

There is now a relatively new wikipage on solution information.  I have a few 
small requests and hope people could oblige.

Solution information

  http://en.wikibooks.org/wiki/GLPK/Solution_information

  - a general review please

Karush-Kuhn-Tucker optimality conditions

  
http://en.wikibooks.org/wiki/GLPK/Solution_information#Karush-Kuhn-Tucker_optimality_conditions

  - the "Requirement" table needs careful checking
    (noting that this is brief explanation!)

Sensitivity analysis report

  
http://en.wikibooks.org/wiki/GLPK/Solution_information#Sensitivity_analysis_report

  - the two "Rows" and "Columns" tables need careful checking

  - just a question (for my interest mostly): does this
    process involve re-solving the model using slightly
    different values? .. and if so, is it
    computationally expensive?

Adaptive use

  http://en.wikibooks.org/wiki/GLPK/Solution_information#Adaptive_use

  - anyone care to contribute?

Either make the changes directly, post back to this list, or email me off-line.

TIA, Robbie
---
Robbie Morrison
PhD student -- policy-oriented energy system simulation Technical University of 
Berlin (TU-Berlin), Germany University email (redirected) : address@hidden
Webmail (preferred)           : address@hidden
[from Webmail client]



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