# interdependence of decision variables

Dear all,

its quite clearly stated that independence of decision variables are necessary for solving optimization problems using the simplex method.

Is this a requirement for all linear optimization techniques? And if so, what methods could be used to bypass this requirement. I have been able to solve such problems using exhaustive search and by heuristic techniques, but I would be grateful if someone could point me towards some good papers regarding optimization with interdependencies between decision variables.

Where is that stated? I don't know what you mean by "independence of decision variables". The simplex method can be used to solve linear programming problems with inequality and/or equality constraints on the decision variables. If, say, $x_1 + x_2 = 1$ is one of the constraints, do you consider $x_1$ and $x_2$ to be "independent"? –  Robert Israel May 26 '11 at 19:58