Thread Subject: Can an objective function be zero?

can an Objective function be zero? If yes, what can we infer
from the values of the individual variables that we get
after optimization using linear programming? If no, why?

"Sameer VK" <sameervk.iitkgp@gmail.com> wrote in message
<g2b1dt$46m$1@fred.mathworks.com>...
>
>
> can an Objective function be zero? If yes, what can we infer
> from the values of the individual variables that we get
> after optimization using linear programming? If no, why?

Why not? Its just a number, like any other.
The fact that zero is the additive identity
does nothing here.

It tells you nothing, although an exact zero
is unlikely. Assuming that you have not
made an error by providing a zero vector
for f, or that you have made a sign error
in defining your problem, there is no
information content in a zero.

John

"Sameer VK" <sameervk.iitkgp@gmail.com> wrote in message
<g2b1dt$46m$1@fred.mathworks.com>...
>
>
> can an Objective function be zero? If yes, what can we infer
> from the values of the individual variables that we get
> after optimization using linear programming? If no, why?

I assume you mean specifing an objective function. When the
objective function is 0 (or any other constant), the
optimization problem becomes a feasibility problem, e.g.
check if there exists a solution which respects the
constraints. Once such a solution is found, the algorithm
just exits, with any feasible x.

E.g. min 0
s.t. 1<x<2

The result could be any x between (1,2).

min 0
s.t. x>2
     x<1

is an infeasible problem, for which no x exist.

I have no idea how Matlab's optimization functions handle
these cases.

Cheers,
Sebastiaan

"Sebastiaan " <s.breedveld@erasmusmc.REMOVE.BOO.BOO.nl> wrote in
message <g2b71t$ru8$1@fred.mathworks.com>...
> "Sameer VK" <sameervk.iitkgp@gmail.com> wrote in message
> <g2b1dt$46m$1@fred.mathworks.com>...
> >
> >
> > can an Objective function be zero? If yes, what can we infer
> > from the values of the individual variables that we get
> > after optimization using linear programming? If no, why?
>
> I assume you mean specifing an objective function. When the
> objective function is 0 (or any other constant), the
> optimization problem becomes a feasibility problem, e.g.
> check if there exists a solution which respects the
> constraints. Once such a solution is found, the algorithm
> just exits, with any feasible x.
>
> E.g. min 0
> s.t. 1<x<2
>
> The result could be any x between (1,2).
>
> min 0
> s.t. x>2
> x<1
>
> is an infeasible problem, for which no x exist.
>
> I have no idea how Matlab's optimization functions handle
> these cases.


Interesting. I'd interpret the OP's question as one
where he found f'*x was exactly 0. Since this means
only that f and x are orthogonal to each other, or
that x was identically zero at the returned point.

If the OP has set the objective function to a fixed
constant then it means something entirely different.
You are not optimizing anything at that point, the
algorithm will stop at any feasible point.

I'd ask the OP to tell us what they really meant.

John