Vektorinis optimizavimas

Maksimizuojam vektorine tikslo funkcija

$$\begin{eqnarray}f(x)=(f_i(x),\ i=1,...,m). \end{eqnarray}$$

Pareto optimumas tai aibe $X^*$.
$x^* \in X^*$, jei neatsiras tokio $x$, kad

$$\begin{eqnarray}f_i(x) \ge f_i(x^*),\ \forall i\\ f_j(x) > f_j(x^*),\ \exists j \end{eqnarray}$$

Skaliarizacija:

$$\begin{eqnarray}x(c)= arg \max_x \sum_i c_i f_i(x) \\ c_i >0 \end{eqnarray}$$

Cia $x(c) \in X^*$
Ribojimai:

$$\begin{eqnarray}x(b)= arg \max_x f_1(x)\\ f_i(x) \ge b_i, \ i=2,...,m \end{eqnarray}$$

Cia $x(b) \in X^*$, jei $x(b)$ vienintelis.