What are some good references for mathematical optimization for the layman?
This is a very vast topic. For nonlinear optimization the book by Bertsekas is a standard reference. For convex optimization you should look at Boyd and Vandenberghe. For linear programming, the book by Schrijver is a reasonable (but dense) source. 

But you should also look at course material. Each of the authors mentioned above also has course material/lecture slides that might be useful.