- Instructors: Ketan Rajawat
- Prerequisites:
Linear Algebra, Probability
**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.
- References:
- Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge University Press. [Online]. http://www.stanford.edu/~boyd/cvxbook/
- Convex Optimization in Signal Processing and Communications, D. P. Palomar, Y. C. Eldar. Cambridge Press, 2010.
- IEEE Signal Processing Magazine- Special Issue on Advances in Convex Optimization, Vol. 27, No. 3, May 2010.
- Dimitri P. Bertsekas, Convex Analysis and Optimization, Athena-Scientific, 2003.
- Format (tentative)
- Major quiz (10) scheduled on 6 Feb. (Monday)
- Mid-sem exam (20) schedule TBA
- End-sem exam (35) schedule TBA
- 7 Assignments (10)
- 1 Term paper (25)
- Time and place: Monday 11am, Thursday, Friday 10am, L17
- 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
- Tentative list of topics for Term Paper
- Convex optimization in game theory
- Total least squares
- Nonlinear classification via kernel methods
- Integer programming techniques
- Majorization-minimization technique for solving non-convex problems
- FIR filter design
- Multiobjective optimization, pareto optimality
- Capacity-rate distortion duality and interpretation
- Robust optimization
- Signomial programming in power control
- Difference of convex programming
- Face detection/recognition via SVMs
- Numerical algorithms for L1 norm minimization
- Semidefinite relaxation for quadratic optimization problems
- Principal compoenent analysis and applications
- Convex optimization is speech processing/recognition
- Convex optimization applications in image processing
- Distributed convex optimization for resource allocation in networks
- Network flow problem, total unimodularity, network simplex
- Gradient descent algorithm, Newton method, and convergence resutls
- Real-time convex optimization in signal processing
- Stochastic gradient descent and convergence
- Learning sparse dictionaries for image compression
- Cross-layer optimization for resource allocation in networks
- Convex optimization in finance
- Alternating minimization and coordinate descent methods
- Augmented Lagrangian method
- Behind cvx: self-dual minimization, interior point methods
- Convex optimization applications for ML estimation
- Genetic algorihtms for non-convex optimization
- SDP relaxation detectors for MIMO systems
- Algorithms for low-rank matrix factorization
- Nonnegative blind source separation
- Convexity and submodularity
- Robust adaptive beamforming
- Solving very large-scale convex optimization problems
- Subgradient method and applications
- Saddle point methods for convex optimization
- Convex optimization for visualizing high dimensional data