Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May., 2019
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 #2
Assigned: Jan. 17th, 2019
Due: Jan. 24th, 2019
Points: 80
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. 20 points
    Solve the single-variable minimization problem given below and explore with it duality of the Lagrangian and sensitivity concept of the Lagnrage multiplier. Plots and insightful explanations are expected.

  2. 30 points
    Write down five linear inequality constraints for which the shaded pentagon shown in the firgure velow is the feasible region. Now, consider f = y - mx as the objective function. Find the ranges of m for which vertices, A, B, C, D, and E are the minimizing points to minimize f.

  3. 30 points
    Solve the two-variable minimization problem with two inequality constraints given below. Find the ranges of "alpha" for which, at the minimizing point, only g1 active, only g2 is active, and both g1 and g2 are active. Solve it analytically, graphically (in Matlab), and numerically (using fmincon). Extra points if you can guess the origin of this problem in structural optimization.