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

From: Robbie Morrison
Subject: Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations)
Date: Fri, 13 May 2011 00:39:43 +1200 (NZST)
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Hello Andrew, also Marc and the list

To:          Robbie Morrison <address@hidden>
Subject:     RE: [Help-glpk] optimality conditions paragraph (KKT and LP
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:

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:

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:

  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,

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
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