f({{x}_{1}},{{x}_{2}},...,{{x}_{n}})={{c}_{1}}{{x}_{1}}+{{c}_{2}}{{x}_{2}}+...+{{c}_{n}}{{x}_{n}}\to \min

\left\{ \begin{matrix}

a_{11}{x}_{1}+{a}_{12}{x}_{2}+...+{{a}_{1n}}{{x}_{n}}\ge {{b}_{1}}, \\

{a}_{21}{{x}_{1}}+{{a}_{22}}{{x}_{2}}+...+{{a}_{2n}}{{x}_{n}}\ge {{b}_{2}}, \\

... \\

{{a}_{m1}}{{x}_{1}}+{{a}_{m2}}{{x}_{2}}+...+{{a}_{mn}}{{x}_{n}}\ge {{b}_{m}}, \\

\end{matrix} \right.

f({{x}_{1}},{{x}_{2}},...,{{x}_{n}})={{c}_{1}}{{x}_{1}^2}+{{c}_{2}}{{x}_{2}^2}+...+{{c}_{n}}{{x}_{n}^2}\to \min

\left\{ \begin{matrix} a_{11}{x}_{1}+{a}_{12}{x}_{2}+...+{{a}_{1n}}{{x}_{n}}\ge {{b}_{1}}, \\ {a}_{21}{{x}_{1}}+{{a}_{22}}{{x}_{2}}+...+{{a}_{2n}}{{x}_{n}}\ge {{b}_{2}}, \\ ... \\ {{a}_{m1}}{{x}_{1}}+{{a}_{m2}}{{x}_{2}}+...+{{a}_{mn}}{{x}_{n}}\ge {{b}_{m}}, \\ \end{matrix} \right.

f({{x}_{1}},{{x}_{2}},...,{{x}_{n}})={{c}_{1}}{{x}_{1}}+{{c}_{2}}{{x}_{2}}+...+{{c}_{n}}{{x}_{n}}\to \min

\left\{ \begin{matrix} a_{11}{x}_{1}+{a}_{12}{x}_{2}+...+{{a}_{1n}}{{x}_{n}}\ge {{b}_{1}}, \\ {a}_{21}{{x}_{1}}+{{a}_{22}}{{x}_{2}}+...+{{a}_{2n}}{{x}_{n}}\ge {{b}_{2}}, \\ ... \\ {{a}_{m1}}{{x}_{1}^2}+{{a}_{m2}}{{x}_{2}^2}+...+{{a}_{mn}}{{x}_{n}^2}\ge {{b}_{m}}, \\ \end{matrix} \right.