Editing Nonlinear programming (section)

===3-dimensional example===
[[Image:Nonlinear programming 3D.svg|thumb|right|The tangency of the top surface with the constrained space in the center represents the solution.]]
Another simple problem (see diagram) can be defined by the constraints
<math display="block">\begin{align}
x_1^2 - x_2^2 + x_3^2 &\leq 2 \\
x_1^2 + x_2^2 + x_3^2 &\leq 10
\end{align}</math>
with an objective function to be maximized
<math display="block">f(\mathbf x) = x_1 x_2 + x_2 x_3</math>
where {{math|1='''x''' = (''x''<sub>1</sub>, ''x''<sub>2</sub>, ''x''<sub>3</sub>)}}.