Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May., 2015
Instructor: G. K. Ananthasuresh , Room 106, ME Building, suresh at mecheng.iisc.ernet.in
Lectures: Tu, Th: 08:30 AM - 10:00 AM; Venue: ME MMCR (Multimedia Classroom)

Homework #4
Assigned: Jan. 27th, 2015
Due: Feb. 3rd, 2015
Points: 50
Additional points for work that is beyond instructor's expectation!
Look up Homework #1 of 2010 offering of this course and the solution posted there to know what is meant by "beyond instructor's expectation".

1. 30 points
   Soap films are adept at solving calculus of variations problems of a certain kind--surface with minimal surface area bound by a given space curve. Try to compete with a soap film in terms of accuracy if not speed. Take a piece of wire and bend it to any shape you like and dip into soap water to create a minimal surface. Take a photograph of it. Now, compute that surface by solving a finite-variable optimization problem. The soap film and your solution should look the same.
2. 20 points
   Soap films also solve topological problems--the famous Steiner Tree problem . Formulate this problem for arbitrary number of points as a calculus of variations problem or a finite-variable optimization problem so that the resulting solution gives the optimal topology in addition to the shape of the minimal surface of the soap-film or minimum-distance conectivity among the points. Just formulate; no need to solve. If you also solve, you get bonus points as usual.