Editing Nonlinear programming (section)

===2-dimensional example===

[[Image:Nonlinear programming.svg|200px|thumb|right|The blue region is the [[feasible region]]. The [[tangent line|tangency]] of the line with the feasible region represents the solution. The line is the best achievable [[contour line]] (locus with a given value of the objective function).]]
A simple problem (shown in the diagram) can be defined by the constraints
<math display="block">\begin{align}
x_1 &\geq 0 \\
x_2 &\geq 0 \\
x_1^2 + x_2^2 &\geq 1 \\
x_1^2 + x_2^2 &\leq 2
\end{align}</math>
with an objective function to be maximized
<math display="block">f(\mathbf x) = x_1 + x_2</math>
where {{math|1='''x''' = (''x''<sub>1</sub>, ''x''<sub>2</sub>)}}.