\(\begin{array}{ll}\operatorname{minimize} & f_0(x) \\ \text { subject to } & f_i(x) \leq b_i, \quad i=1, \ldots, m .\end{array}\)
As an important example, the optimization problem (1.1) is called a linear program if the objective and constraint functions \(f_0, \ldots, f_m\) are linear, i.e., satisfy
\[f_i(\alpha x+\beta y)=\alpha f_i(x)+\beta f_i(y) \]for all \(x, y \in \mathbf{R}^n\) and all \(\alpha, \beta \in \mathbf{R}\).