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

From: Andrew Makhorin
Subject: Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations)
Date: Thu, 12 May 2011 23:44:26 +0400

> A book by Dantzig and Thapa uses standard form to apply to equality
> constraint version:
> 20programming%22&pg=PA48#v=onepage&q=standard%20form&f=false
> See page 48

It is funny, but I noticed a typo just on p.48. In the dual (2.17) there
must be no constraint "x >= 0". In fact, the dual can be written as

        Maximize b'pi
        s.t.     A'pi + lambda = c
                 lambda >= 0, pi is of any sign

>From the second line it follows that A'pi = c - lambda, so considering
lambda as slacks we have:

        Maximize b'pi
        s.t.     A'pi <= c
                 pi is of any sign

x is a vector of primal variables, so it cannot appear in the dual.

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