Re: LinearProgramming unbounded

• To: mathgroup at smc.vnet.net
• Subject: [mg65699] Re: [mg65682] LinearProgramming unbounded
• From: jackgoldberg at comcast.net
• Date: Sun, 16 Apr 2006 01:44:58 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Andrea,

A standard linear program (non-negative variables, linear equality constraints and a linear objective function) can stop for two reasons:  1) The simplex algorithm reaches an optimal solution or 2) the objective function's max (min) is +infinity (-infinity).
In other words, there is an infinity of non-negative solutions and as some of these variables tend to infinity, the objective function tends to + or - infinity depending on whether the problem is a max or min.

I have no idea if this is your problem; I am simply posting that a linear program can yield unbounded solutions.  When this happens, it is usually the result of a modelling error.  Are all your variables non-negative?

-------------- Original message ----------------------
From: andrealk at gmail.com
To: mathgroup at smc.vnet.net
> Hello all -
>
> I have run into what I hope is an easily resolved problem.  I am using
> the LinearProgramming function to maximize an objective function, which
> in the code below is called "objfcn".  "S" is a matrix representing the
> equations with 761 rows and 1320 columns; "zerovector" is a vector, one
> column and 761 rows, where each element is {0,0}, meaning that each
> equation is exactly equal to zero; "constraints" is a list of 1320
> constraints.  I have used LinearProgramming successfully in many
> instances.  However, I now get an error saying that the system in
> unbounded.  How can that be?  As far as I can tell my dimensions are
> all correct.
>
> Does anyone have any suggestions?  Has anyone had a similar problem?
> Below is what the code looks like.
>
> LinearProgramming[-objfcn, S, zerovector, constraints]
>