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

[Robbie Morrison]

Hello Andrew, also Marc and the list

------------------------------------------------------------
To:          Robbie Morrison <address@hidden>
Subject:     RE: [Help-glpk] optimality conditions paragraph (KKT and LP
formulations)
Message-ID: <address@hidden>
From:        Andrew Makhorin <address@hidden>
Date:        Thu, 12 May 2011 12:08:03 +0400
------------------------------------------------------------

> Hi Robbie,
>
> [snip: earlier post]
>
> Probably to make the glpk wikibook paragraph about the KKT conditions
> complete, the text following below could be included there (' means
> transposition).
>
> Best regards,
>
> Andrew Makhorin
>
> Original (primal) LP problem in the standard format:
>
>    minimize  z = c'x
>
>    s.t.     Ax = b
>
>              x >= 0
>
> where x is a vector of primal variables.

[snip: remainder of post]

---------------------------------
 KKT theory
---------------------------------

The new mark-up is here:

  
http://en.wikibooks.org/wiki/Talk:GLPK/Solution_information#Karush-Kahn-Tucker_theory

A couple of small points (which can be easily reversed):

  * used the term "augmented form" instead of "standard format"

  * changed (pi, lambda) to (pi | lambda) for the vector concatenation

  * added a final sentence on MIP use

Thanks too to Marc for his encouragement.

---------------------------------
 Status "B"
---------------------------------

One other thing, somewhat related.  From the same page
describing the various GLPK human-readable reports.

More specifically, the 'glp_print_sol' solution report,
also accessible via the GLPSOL '--output' option.  For
an example, please see:

  http://en.wikibooks.org/wiki/GLPK/Interoperability#GLPSOL_output_format

What does 'B' in the 'St' status column indicate?

Is this identical to the 'BS' in the same column, in
the sensitivity analysis report produced by
'glp_print_ranges' and the '--ranges' option?  For an
example, see:

  http://en.wikibooks.org/wiki/GLPK/Interoperability#GLPSOL_sensitivity_analysis

  BS = constraint inactive

In addition, there can be "< eps" comments.  For
close-to-zero values, I guess.  What is the threshold?
Is this threshold user-modifiable?  If so, how can it
be reset?

Also, often the 'Lower bound' and 'Upper bound' entries
are missing, I suppose this implies -inf and +inf,
respectively?

best wishes to all
---
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]