Re: [Help-glpk] control parameters and round-off error

[Ali Baharev]

> > My LP problems are generated by successive linearization of a
> > nonlinear problem, and i need to automate the solution process. So my
> > problem is not only for this particular LP problem, i need an error
> > estimate on the objective function value for each solved LP problem.
>
> I think that in this case one should talk about _approximation_ error,
> not about round-off error.

Sorry, i don't get it. Approximation error is enclosed by an interval
in my case, or i do not know what you mean by approximation error.

One can enclose all possible function values of a nonlinear function
in a given box (domain) with linear constraints with absolute
certainty (100.0% sure) using interval arithmetic and directed
rounding. Please visit e.g.

http://www.nd.edu/~markst/publications.html

Y. Lin and M. A. Stadtherr, "LP Strategy for Interval-Newton Method in
Deterministic Global Optimization," Ind. Eng. Chem. Res., 43,
3741-3749 (2004).

As i don't know the solution to my nonlinear problem with guaranteed
accuracy, i cannot locate that LP step of several thousands which
discards the solution. One thing is sure, the problem has a solution
and it is lost somewhere. I suspected which LP problem it was, but
with lpx_exact i could prove that the solution to that particular LP
problem is correct.

I can hardly imagine a better way than checking all solutions of the
LP problems with interval arithmetic and directed rounding, as it is
written e.g. here:

http://www.ti3.tu-harburg.de/cgi-bin/cjbibsearch/publications/ti3.html?author=jansson

C. Jansson. Rigorous Lower and Upper Bounds in Linear Programming.

I will get back to this problem as soon as i know the solution vector
to my original nonlinear problem so that i can identify the
problematic iteration step discarding the solution vector.

Thank you for your time and kind help,

Ali