Abstract
Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers. Near-optimal robust versions of multilevel problems are shown to remain in the same complexity class as the problem without near-optimality robustness under general conditions.
Highlights
Multilevel optimization is a class of mathematical optimization problems where other problems are embedded in the constraints
We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers
We have shown that for many configurations of bilevel and multilevel optimization problems, adding near-optimality robustness to the canonical problem does not increase its complexity in the polynomial hierarchy
Summary
Multilevel optimization is a class of mathematical optimization problems where other problems are embedded in the constraints. Because the set of near-optimal lower-level solutions potentially has infinite cardinality and depends on the upper-level decision itself, near-optimality robustness adds generalized semi-infinite constraints to the bilevel problem.
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