# Finding the dual of the inner problem in robust linear optimization

I am trying to understand robust linear program, specifically the dual of the inner program. Can somebody help me understand the equality, in the dual for the inner maximization problem. Since, in duality >= is replaced by <= and vice versa.

Robust inner LP Dual

• Your understanding of LP duality is incorrect. In LP duality, inequality constraints in the primal become sign constraints on dual variables, while sign constrained variables in the primal correspond to inequality constraints in the dual (and free primal variables correspond to equality constraints.) Sep 13, 2017 at 18:49
• which means the free constrained variables in the innner max program is responsible for creating that equality. If by chance the variables in the primal are constrained to have only positive values, then the equality will get replaced by inequality?? and if so that >= or <=. Can you direct me to a book or a reference where i can get a clear understanding of this? Sep 13, 2017 at 18:56
• Yeah got it. i think i can follow from the table given in this discussion math.stackexchange.com/questions/234575/… Sep 13, 2017 at 19:04
• Thanks, this was really helpfull, Thanks Brian Sep 13, 2017 at 19:05