Week 12- Duality
Welcome to Week 12. During this week we will cover sections 5.1, 5.2, 5.4.3, 5.4.4, 5.5.2, and 5.6, which are about a topic called duality. Duality is a technique that transforms constrained optimization problems into new forms by introducing Lagrange multipliers for their constraints. These dual optimization problems can provide lower bounds on non-convex optimization problems and can also provide equivalent formulations for convex optimization problems. However, the most useful aspect of duality in practice is that it enables a sensitivity analysis of the optimal value of the objective to the value of the constraints. Each constraint has a shadow price that comes from the solution to the dual problem which says how much the objective could be lowered if that constraint was weakened. We talk about duality in general and show several examples of how to use it to gain deeper knowledge about optimization problems.
Your sixth homework assignment is due Sunday April 27th at midnight.
Here are more details on what you need to do this week:
- Go through module 11 and complete the week 12 readings.
- Attend our second meetup on Monday at 6:45 p.m. ET on Zoom
- Finish working on Lab 6