What is the difference between options objective_bound and objective_target?

[rschwarz]

I see two options named objective_bound and objective_target, but I can't clearly identify their meaning from the descriptions alone.

In particular, I'd like to know which of the two (if any) is equivalent to Gurobi's cutoff, ie, pruning nodes with a dual bound worse than the given value.

I'm guessing that objective_bound is the better fit.

But what would objective_target mean, then? Is it a termination criterion for stopping when a solution at least as good as the target was found?

[jajhall]

When the dual simplex objective (for a dual feasible point) reaches the objective bound then the algorithm terminates. There is a guarantee that the optimal (primal) objective value can be no better than objective bound. Indeed, in general, it will be worse than this value.

The objective_target is an (unimplemented) option for the primal simplex solver. What it will do is stop the primal simplex solver when the primal objective (for a primal feasible point) reaches the objective_target. There is a guarantee that the optimal (primal) objective value is at least the objective target. Unlike the objective_bound, the objective_target is a value that's actually attained. Hence the different names. Gurobi appears to use Cutoff for both, but I prefer the distinction.

[rschwarz]

Thanks for the explanation. So in the context of MIP solving, is the value of objective_bound is then used for all node relaxations, effectively pruning nodes worse than this bound?

[jajhall]

In the MIP solver there's a known best dual bound (from a node solution) that's used to prune nodes that can't be better and also used to set objective_bound so that when nodes with a better dual bound are solved, the dual simplex solver doesn't run longer than necessary.