Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May., 2018
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

Homework #3
Assigned: Jan. 25th, 2018
Due: Feb. 1st, 2018
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. 7 + 7 = 14 points
    (a) Find the solution(s) of minimizing f = -x subject to h = x3+y2 = 0 . Use necessary and sufficient conditions. Draw the contours and the constraint curve.
    (b) Find the minima of f = -x2y2z2 subject to h = x2+y2+z2 - 3 = 0 . Use necessary and sufficient conditions.
  2. 36 points
    Here is a puzzle that can be solved using continuous optimization. Consider the self-avoding path on a 5x5 grid.
    .
    Each grid point can be occupied by beads labelled as H or P. Assume that you have 12 H beads.The rest are P beads. Where would you place H beads to minimize E defined as follows?
    E = sum of all Eij where i and j are grid numbers that are adjacent (in the two orthogonal grid directions but not diagonally) to each other but are not connected by the path. Eij = 0 if two P beads are there, -1 if H-P or P-H beads are there, -2.3 if H-H beads are there are at i and j grid points.