$${{\mathcal {D}(\mathcal {C})}}$$ -optimization and robust global optimization

Abstract

For solving global optimization problems with nonconvex feasible sets existing methods compute an approximate optimal solution which is not guaranteed to be close, within a given tolerance, to the actual optimal solution, nor even to be feasible. To overcome these limitations, a robust solution approach is proposed that can be applied to a wide class of problems called $${{\mathcal {D}(\mathcal {C})}}$$ -optimization problems. DC optimization and monotonic optimization are particular cases of $${{\mathcal {D}(\mathcal {C})}}$$ -optimization, so this class includes virtually every nonconvex global optimization problem of interest. The approach is a refinement and extension of an earlier version proposed for dc and monotonic optimization.