DOI link for Optimization
Classical optimization involves ﬁnding the minimum or maximum of a function ϕ : D ⊂ Rn → R with respect to its argument x ∈ Rn. The function ϕ is called the objective function. Sometimes, there are no restrictions on the argument x, in which case the problem is said to be unconstrained . Often there are side conditions, or constraints, expressed as inequalities and equations; the problem is then said to be constrained . A general optimization problem can be expressed as
minimize ϕ(x) subject to ci(x) = 0, i = 1, . . . ,m1,
gi(x) ≤ 0, i = 1, . . . ,m2, where ϕ : D → R and ci, gi : D → R, and x = (x1, . . . , xn)T .