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Re: [Help-glpk] Re: Initial Basis

From: Michael Hennebry
Subject: Re: [Help-glpk] Re: Initial Basis
Date: Mon, 28 Mar 2011 11:25:34 -0500 (CDT)
User-agent: Alpine 1.00 (DEB 882 2007-12-20)

On Mon, 28 Mar 2011, Andrew Makhorin wrote:

Suppose I solve a linear programming problem with the simplex
algorithm, then change a row of coefficients. I then change the
previously found optimal basis slightly or not at all (by one or zero
variables -- both cases are relevant here) so that the new basis is
primal feasible. Given how little I changed from the first problem, it
seems that I should be able to solve a second one without having to
restart from scratch. Is this possible?

Yes. If you change a row, the optimal basic solution may either remain
optimal or become primal infeasible, but in both cases it remains dual
feasible, so you can reoptimize the modified lp with the dual simplex

Suppose the constraint's slack is nonbasic
and one negates all the coefficients.
I'm pretty sure that that would make it dual infeasible.

Michael   address@hidden
"Pessimist: The glass is half empty.
Optimist:   The glass is half full.
Engineer:   The glass is twice as big as it needs to be."

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