# Constraint optimization problem

The general aim for constraint optimization problem is to find an optimal solution to a set of constraints subject to some objective function obj. For example, consider a CSP $LaTeX: P = \{ C, x_1 \in D_1, \dots, x_n \in D_n\}$ together with a function $LaTeX: obj : Sol \to \mathbb{R}$. $LaTeX: obj$ is a mapping from solutions to $LaTeX: P$ (i.e., all elements the set $LaTeX: Sol$) to the set of real numbers, $LaTeX: \mathbb{R}$.
A solution, $LaTeX: d$, to a constraint optimization problem is a complete assignment of variables that satisfies all constraints $LaTeX: C \in P$ and for which the value $LaTeX: obj(d)$ is optimal (either minimal or maximal, depending on the sense of the optimization).