### SC 607 – OPTIMIZATION

**Course offered in:**

Spring 2017

**Instructors:**

Prof. Ankur Kulkarni

**Course Content:**

Convex analysis and review of real analysis, Optimization in Euclidean space: linear programming, integer programming, bilinear programming, duality, constrained optimization, convex optimization, constraint qualification, KKT conditions, geometric theory of duality

Algorithms and convergence- Simplex method (for linear programming), Sequential convexification, lift and project method (for binary programs), Active set method (Quadratic programming), Line search method (unconstrained optimization), Constrained optimization (Barrier, Penalty, Cutting plane method, Augmented Lagrangian methods), Interior point method

**Prerequisites:**

Linear algebra, real analysis and some comfort with mathematical reasoning. For UGs, consent of instructor is mandatory. The prerequisites aren’t necessarily rigid, but you should be motivated enough to take up the course.

**Feedback on Lectures:**

The lectures were extremely well structured. Relevant concepts, proofs and examples were meticulously explained on the board. Lectures were very interactive and the instructor gave the students enough time to absorb the concepts. The instructor was very receptive to doubts.

As a part of the course, each of us was required to volunteer for taking notes of one lecture as per the prescribed format. Before endsem, all the lecture notes were made available for reference.

**Feedback on Tutorials, Assignments and Exams:**

The assignments played a very crucial part in the learning process. Each problem was an illustration of some important concept taught in the class. The difficulty was moderate and on occasions, the assignments were quite lengthy. Leaving the assignments for the last moment is discouraged.

There was only a single end-semester exam worth 50 marks. The questions were mainly a random selection from the homework problems and problems discussed in class with minor changes. This format was revealed beforehand. Sincerely solving assignments and going through class notes is a must for scoring well in the exam. But speed is also important as there were some questions on algorithms which demanded tedious calculations.

**Difficulty:**

The course was easy before Midsem. The next part of the course was difficult or fast paced.

**Grading Statistics:**

Moderate grading. You can refer to Asc for more details.

For obtaining an audit grade, one was expected to submit assignments and scribe notes.

**Study Material and References:**

Primary reference book:

- S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004

Other references, for specific sections:

- J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2006
- Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli, Integer Programming, Springer 2014
- D. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, 1984

**Takeaways from the course:**

The following description presented by the instructor on the course page sums up the importance of this course,

“I optimize, therefore I am”

The urge to optimize is fundamental to our being. If we exist, we think. If we think, we make choices. If we make choices, we want to optimize. Indeed, optimization may also be fundamental to what makes our being. Laws governing the behavior of physical (and hence biological) systems seem to have the character of seeking to optimize some energy functional.

This course will provide an understanding of the theory of mathematical optimization and some landmark algorithms. Throughout the emphasis will be on the geometry of the problem and uncovering geometric obstructions to the success of algorithms.”

It’s needless to say that the skills learnt in this course would definitely come in handy in Electrical Engineering and allied fields.

Review by – Mansi Sood, 5th year Undergrad, DD CSP (mansisood01@gmail.com)