This paper proposes a method for the solution of constrained min-max problems. The method is tested on a benchmark of representative problems presenting different structures for the objective function and the constraints. The particular min-max problem addressed in this paper finds application in optimisation under uncertainty when the constraints need to be satisfied for all possible realisations of the uncertain quantities. Hence, the algorithm proposed in this paper search for solutions that minimise the worst possible outcome for the objective function due to the uncertainty while satisfying the constraint functions in all possible scenarios. A constraint relaxation and a scalarisation procedure are also introduced to trade-off between objective optimality and constraint satisfaction when no feasible solutions can be found.
|Number of pages||47|
|Journal||Optimization and Engineering|
|Early online date||2 Apr 2021|
|Publication status||E-pub ahead of print - 2 Apr 2021|
- constrained min-max
- worst case scenario
- constraint relaxation