Nonconvex constrained optimization by a filtering branch and bound

Amajor difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the aBB-algorithm for single-objective optimizationmay fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In thiswork, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective alpha BB method fails, i.e., it terminates without ever finding a feasible solution.

Automated summary

The difficulty in dealing with optimization problems with nonconvex constraints lies in finding feasible solutions. Introducing a filtering approach inspired by a multiobjective reformulation, the trade-off between constraint satisfaction and objective value can be identified, leading to the discovery of feasible and often optimal solutions where traditional methods fail.