Given a domain D on the plane and a real-valued *height* function defined
on the boundary of D, the problem is to find the surface that has the given
boundary values and that minimizes the surface area. This problem is convex and
can be easily converted to a second-order cone optimization problem.

The specific problem coded in the models below takes D to be a square and the boundary height function to be concave quadratic on each of the four sides.

*file:*minsurf.mod*file:*minsurf_socp.mod*file:*minsurf_nonconvex.mod*file:*minsurf_exp.mod

The output from these models `height.wrl`

was used to produced the
3-D vrml model that you can view by clicking on the image below.