Course Objective:
This course is appropriate for both upper-level undergraduates and graduate students with basic knowledge in matrix theory (linear algebra) and calculus. Optimization is a very important subject which finds applications in many branches of science and engineering, to name a few, economics, computer science, financial engineering, systems engineering, electrical and computer engineering, mechanical engineering. The course aims to equip students with practical optimization methods for solving real-world applications and prepare them for a career in academia and industry. Topics to be covered include linear programming, nonlinear programming, calculus of variations and dynamic programming.
Prerequisites:
The course is offered as a first-year graduate level course. Basic knowledge of linear algebra, calculus and differential equations and scientific computing is assumed.
Grading:
- Homework: 15%
- Midterm Exam: 25%
- Final Exam: 40%
- Project: 20%
Textbooks:
[BV] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
Available online at http://www.stanford.edu/~boyd/cvxbook/
[DL] D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
Available online at http://liberzon.csl.illinois.edu/teaching/cvoc/cvoc.html
Supplementary Textbooks:
[MI] M. D. Intriligator, Mathematical Optimization and Economic Theory, SIAM Classics in Applied Mathematics, 2002.
[LY] D. Luenberger and Y. Ye, Linear and Nonlinear Programming, Springer, 2008.
[CZ] E. K. P. Chong and S. H. Zak, An Introduction to Optimization, John Wiley & Sons Inc., 4th edition, 2013.
Additional References:
[AF] M. Athans and P. L. Falb, Optimal Control: An Introduction to the Theory and Its Applications, Dover Publications Inc., 2007
[DL] D. Luenberger, Optimization by Vector Space Methods, Wiley, 1997.
[DBa] D. Bertsekas, Nonlinear Programming, Athena Scientific, Second Edition, 1999.
[DBb] D. Bertsekas, Dynamic Programming and Optimal Control. Vol. 1 and 2. Nashua, NH: Athena Scientific, 2007.
[AM] B. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods, Dover, 1990.
[PV] P. Varaiya, Lecture Notes on Optimization, Available online.
Course Schedule:
Lecture 1 Introduction and Basic Concepts
Lecture 2 Unconstrained Optimization
Lecture 3 Convexity and Convex Optimization
Lecture 4 Convex Optimization
Lecture 5 Duality and Linear Programming
Lecture 6 KKT Conditions
Lecture 7 Constrained Nonlinear Optimization
Lecture 8 Numerical Methods and Applications
Lecture 9 Optimal Control and Calculus of Variations
Lecture 10 Calculus of Variations
Lecture 11 Introduction to Dynamic Programming
Lecture 12 Dynamic Programming and Applications
Lecture 13 Maximum Principle
Homeworks:
Exams: