nonlinear programming with inequality constraint I am confused about a nonlinear programming constrained to the region
$$X = \{(x1,x2) \in\mathbb{R}^2: (x1^2/a^2)+(x2^2/b^2)<=1\}$$
Can anyone show the steps of solving such a problem (for some arbitrary objective function)? 
Is there any special property of this constraint? 

Yes, your feasible set is convex. Whether this helps you will depend on your objective function (and in particular, on whether the objective is also convex.)
Because your constraint is so simple, one general approach is to try both cases where the constraint is active or inactive:


*

*Ignore the constraint and solve the unconstrained optimization problem (this may or may not be challenging in and of itself, depending on how nasty the objective function is.) For each solution, check if it lies inside the ellipse.

*Maximize(/minimize) the objective function on the boundary of the feasible region, which in this case has the easy parameterization $x1 = a\cos\theta, x2 = b\sin \theta.$ For each solution, check that the gradient of the objective function at the solution points out of(/into) the ellipse.
