Optimization problem

The general nonlinear optimization problem [1] can be formulated as follows: find a minimum of the objective function ϕ(x), where x lies in the intersection of the N-dimensional search space

and the admissible region ℱ ⊆ ℝ^N defined by a set of equality and/or inequality constraints on x. Since the equality g_s(x) = 0 can be replaced by two inequalities g_s(x) ≤ 0 and –g_s(x) ≤ 0, the admissible region can be defined without loss of generality as

References

1. Runarsson T.P., Yao X. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation. 2000. 4(3):284–294