Originally posted by: djami

Hello,

I have a modelling question. I have a resource allocation problem in which I would like to minimize a function subject to each allocation xi either being zero or >= ci, for some ci>0 (i.e. xi =0 or xi>=ci for all i=1,... n). I am having trouble finding any references to these kinds of constraints in the literature. Does anyone know what they are called, and/or can you point me to any books or articles that consider such constraints? (in particular, formulating the Lagrangian etc). 

Thanks in advance.

Your xi are what is known as semicontinuous variables. A web search on that term should yield some references. CPLEX "understands" semicontinuous variables. In the Concert API (Java version), there is an interface IloSemiContVar for them. In the C++ API there's a class with the same name, and I'm sure it exists in other APIs (and probably in OPL) but possibly with different (but similar) names.

Originally posted by: djami

Thanks Paul,  I knew there had to be a simple name!