MS&E 111/ENGR 62: Supplementary Notes

Optimization permeates many (almost all) branches of human endeavor. Darwinian evolution optimizes a species for the “best traits” for survival. Firms optimize their supply chains. Fund managers optimize their portfolios. On a lighter note, personal dating sites try to find the “best match”, and advertisers on online sites try to show you the “best advertisement” based on your user profile. The window arch, the suspension bridge, the coding scheme used by your cell phone, are all highly optimized. This class will largely study Linear Programming (or LPs), one of the simplest and perhaps the most widely used paradigms for optimization. We will see lots of real world problems that can be modeled and solved as Linear Programs. We will study and use properties of LPs such as duality and vertex optimality. We will spend significant amount of time on a special sub-class of LPs, known as network flow problems. Finally, we will use LPs as a base to briefly explore two other important techniques in optimization: Dynamic Programming and Convex Optimization.