In the Ben-Tal Robust optimization book, the approach is called, constraint-wise.
In other words, you treat uncertainty (immunization against uncertainty) in each constraint independently, without loss of generality.
The question in my mind is, when we have a model, say, MINLP,
does the nonconvexity affect the robustness of the solution ( constraint) ?
if I am to explain myself simpler,
in a convex program, our uncertain constraint is replaced by its ( reformulated) Robust Counterpart, then in the end, we have a global robust optimal solution which deterministically ensures feasibility of our constraint ( within uncertainty set).
but, my question is, does this guarantee changes when we have MINLP, regardless of convexity of the constraint with respect to decision variables.
the MINLP solvers will find us a feasible solution of course, but is the robustness of the constraint still deterministically guaranteed ?
I may have not been able to clearly expressed myself, so please let me know if that is the case.
Thanks in advance.
Dear Alireza,
I suggest you to see links in topic.
-Nonconvex Robust Optimization for Problems with Constraints ...
https://pubsonline.informs.org/doi/abs/10.1287/ijoc.1090.0319
-Non-convex optimization and robustness in realtime model predictive ...
onlinelibrary.wiley.com/doi/10.1002/rnc.1216/abstract
-The State of Robust Optimization - Semantic Scholar
https://pdfs.semanticscholar.org/.../1ab84c9993195ddcb6d0f97c1e...
best regards
Thanks Nicolas,
I say it in the simplest way, I just hope that it is adequately technical.
is any feasible solution in a MINLP model ( which is treated constraint-wise and with tractable Robust counterparts), robust feasible too?
This came to my mind, because I intend to solve an MINLP model, with Robust Optimization approach,
So I was wondering if changing to MILP ( with approximations ) adds to solutions' robustness ( although it reduces the model robustness ) .
hope Im not very vague.
Thanks Nicolas for your thoughtful insights and responds, as always.
I will look further in the robustness of MINLP case, and if I found anything interesting I would share it here.
Nicolas Dupin , as I reviewed a little of Ben-Tal RO concepts,
I think when we are reformulating the constraints in an optimization to make it Robust, we are in fact altering the feasible set or region.
I guess every feasible point in the new feasible region is deterministically Robust vis-a-vis the range of uncertainty defined in the uncertainty set, but of course not Robust Optimal.
So the problem in Robust MINLP problems will be finding the Robust (Global) Optimal, not "a" Robust solution.
Hope you correct me if Im wrong. Tnx.
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