> > 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 _______________________________________________ Help-glpk mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-glpk
