The Minimal Surface Area Problem
An Example of Unconstrained Minimization

Description of the minimal surface area problem

The minimal surface area problem is an example of unconstrained minimization. There are no constraints in this problem, like those found in a linear programming problem such as the diet problem. The goal of the problem is to take a given boundary and find the minimum surface that passes through the boundary. The surface that is calculated is what one would expect to see if the boundary had been dipped in bubble solution.

Formulation of problem as unconstrained minimization

• The assumptions about the problem.
• The Verbal formulation
• The Mathematical formulation

Try optimizing for the boundary of your choice

• Choose the fineness of the grid
• Enter the height of the boundary at predetermined points on a square
• The solver will calculate a piecewise linear boundary between the points. The the solver will determine the height of the surface at predetermined points on a grid.
• A picture will be returned of the boundary and the minimal surface through the boundary.

Try me!

Comments and Suggestions

Give us your feedback.

Acknowledgments

The idea for this case study and part of the code was inspired by Minpack-2.

All plots are generated by Gnuplot v3.5.

[ OTC Home Page | NEOS Server | NEOS Guide | Case Studies ]