Objective: Convex optimization has recently been applied to a wide variety of problems in EE, especially in signal processing, communications, and networks. The aim of this course is to train the students in application and analysis of convex optimization problems in signal processing and wireless communications. At the end of this course, the students are expected to:
- Know about the applications of convex optimization in signal processing, wireless communications, and networking research.
- Be able to recognize convex optimization problems arising in these areas.
- Be able to recognize ‘hidden’ convexity in many seemingly non-convex problems; formulate them as convex problems.
- Be able to develop low-complexity, approximate solutions for difficult non-convex problems.
This course will cover (approximately)
- Background on linear algebra
- Convex sets, functions, and problems
- Examples of convex problems: LP, QCQP, SOCP
- Duality, KKT conditions
- Geometric programming and applications
- Linear and quadratic classification
- Network optimization
- Sparse regression, Lasso, ridge regression and applications in image processing
- Robust least squares and applications in signal processing
- Support vector machines and applications in machine learning
- Semidefinite programming and applications in experiment design
- Semidefinite relaxation and applications in MIMO detection, integer programming
- Low rank matrix completion and applications in recommendor systems
- Multidimensional scaling and applications in sensor localization
- Numerical linear algebra, basics of interior point methods