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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:
> http://books.google.com/books?id=jrx3r1qQF8AC&lpg=PP1&dq=%22linear%
> 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
follows:
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.
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), (continued)
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Andrew Makhorin, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Andrew Makhorin, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Meketon, Marc, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Robbie Morrison, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Meketon, Marc, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Andrew Makhorin, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Andrew Makhorin, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Robbie Morrison, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Andrew Makhorin, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations), Meketon, Marc, 2011/05/12
- Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations),
Andrew Makhorin <=