Fundamentals of Optimization

Here are the lecture notes of the course I just finished. Coming from an engineering background, I found this course to be really tough to start with. The 'toughness' didn't change, only I got used to it. The course was graded entirely based on 8 assignments (one every week), which were more an extension of the notes rather than being a completely new devil. I still don't have the big picture or the take-home from the notes, since this course involved pre-requisites such as Linear Algebra and a good enough exposure (supposedly years!) to elements of analysis and advanced calculus, which I didn't have. So most of my time was spent getting a 'feel' for the subject, including notations, concepts et al - basically the 'language of mathematics'. I am still uncomfortable looking at the level of math in the course, but hopefully with more exposure to these kind of courses and materials, I should begin to understand and enjoy the subject more thoroughly.

This is one of a kind course in that it goes into the fundamentals of the subject. Many people (me included) use the word 'optimization' loosely, but hardly realise that there is a whole theory(as I gleaned from this course) that lays the basis for all the algorithms and optimization techniques being widely used in various engineering, science and health disciplines.

A note on my course-mates: Most of them were studs in the field(grad level math course machi)
who left me amazed on their depth in the subject as was evident from the questions fielded in the class. Through this course, I have been fortunate enough to have the experience of knowing first hand how tough Math can be (I had strange opinions on Math before coming here). I might get away with a 3.7 or 3.8 in the course, but you see these assignments were very instructive and guiding the student onto the methodology and analysis required to solve the problems. Ofcourse, I had to understand the theory before attempting the assignment, but as I said earlier the big picture is still missing. I have the bits and pieces from each of these chapters, only I need to piece them together in the coming future.

As a final note, this course(the last course taught by the prof) was taught by a highly knowledgeable prof who was very precise and exact in his development of subject(something new to me since we engineers make a lot of assumptions whenever we can) and as a result, has sort of aroused my interest in optimization theory. Let's see where I can go from here.