Why is Optimization being taught under different titles in different universities?

Question

I am searching for some pdf lecture notes on Optimization:

• Google search

I have found some pdf lecture notes. But, they have various titles like:

• Convex Optimization
• Optimization Methods
• Optimization-I
• Numerical Optimization
• Engineering Optimization
• Mathematical Optimization

Why is Optimization being taught under different titles in different universities or colleges?

What is the significance with the difference in titles?

Answer 1

One important distinction is between "convex optimization" and "nonlinear optimization." From the 1950's through about 2000, most work in nonlinear optimization dealt with methods for finding locally optimal solutions to optimization problems involving smooth (at least twice continuously differentiable) functions. Since then, there has been a major shift in interest towards methods for solving convex optimization problems involving the minimization of convex but not necessarily smooth functions. Some of the lecture notes that you've linked to are specific to convex optimization while others focus more on older approaches to smooth nonlinear optimization.

There are also many other important topics in optimization, including linear programming and the simplex method, interior point methods for linear and conic optimization, combinatorial optimization and integer programming, network flows, stochastic optimization, PDE constrained optimization, and optimal control. Each of these topics is large enough that there are many books on it.

It really shouldn't be surprising that different instructors and authors of textbooks have decided to focus on different aspects of optimization. Depending on your particular interests and needs you should be able to find materials that focus on those areas that are of most importance to you.

Answer 2

Brian Borchers has already provided a good answer, but I'll add some context that is more logistic-related than math-related.

In addition to the fact that optimization is a very large field, it is also extremely practical and currently very much en vogue. As a result, it is completely expected that large universities will run 2 or 3 (I've seen up to 5!) different optimization courses in different departments at the same time.

Although some of these will be very mathematically rigorous and theory-based, the majority of these courses will be application-specific (Industrial/Financial/Engineering Optimization) or designed to only teach enough to get a practical handle on solving optimization problems numerically (Numerical/Computational/Applied Optimization, Optimization Methods/Tools/Techniques).