Abstract
The concept of ?-approximate optimal solution as widely used in nonconvex global optimization is not quite adequate, because such a point may correspond to an objective function value far from the true optimal value, while being infeasible. We introduce a concept of essential ?-optimal solution, which gives a more appropriate approximate optimal solution, while being stable under small perturbations of the constraints. A general method for finding an essential ?-optimal solution in finitely many steps is proposed which can be applied to d.c. programming and monotonic optimization.
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