Keep in mind the method outlined in the AIMMS book is a only an approximation for case of two continuous variables.
Bilinear constraints frequently come up in chemical process applications. For example, decision variables for a particular process stream might be stream flow rate and concentration of a species, and the constraint written on flowrate of that species. These situations lead to non-convex solution spaces that can be solved using global optimization techniques. One way to treat these situations in a linear programming context is to replace the constraint with a set of four linear constraints that provide a convex 'outer approximation'. The outer approximation itself has been known for a long time, and is sometimes called 'McCormick Relaxations.' The approximation can be improved by subdividing the solution space, then using a branch-and-bound search. Repeating this process will eventually give a global solution. The scheme is described in http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.4249 by Ruiz and Grossmann. On Sun, Apr 5, 2015 at 7:22 PM, Antonio Carlos Moretti < [email protected]> wrote: > If the bilinearity involves > > (1) two binary variables or > (2) a binary variable and a continuous variable or > (3) two continuous variable > > then is it possible to write as an integer linear programming. > See ''AIMMS - OPTIMIZATION MODELING' pages 83,84 and 85. (you can get the > pdf through internet) > > Best regards, > Antonio > > >>> Is it possible to solve a problem with bilinear constraints using > >>> GLPK? > >>> > >> > >> No, because bilinear constraints are non-linear while glpk allows only > >> linear ones. > >> > > > > Can we do something about it? From my experience with commercial systems > - > > solving NLP problems involves successive linearisation until convergence, > > although it could lead to a local optimum. > > > > I?d like to participate. > > > > -- > > Ruslan Gazizov > > _______________________________________________ > > Help-glpk mailing list > > [email protected] > > https://lists.gnu.org/mailman/listinfo/help-glpk > > > > > > > _______________________________________________ > Help-glpk mailing list > [email protected] > https://lists.gnu.org/mailman/listinfo/help-glpk >
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