Convex Optimization I
Gain the necessary tools and training to recognize convex optimization problems that confront the engineering field. Learn the basic theory of problems including course convex sets, functions, and optimization problems with a concentration on results that are useful in computation. Develop a thorough understanding of how these problems are solved and the background required to use the methods in research or engineering work.
Solid knowledge of linear algebra as in EE263 and basic probability. Exposure to numerical computing, optimization, and application fields helpful but not required; the engineering applications will be kept basic and simple.
- Optimality conditions, duality theory, theorems of alternative and applications
- Least-squares, linear and quadratic programs, semidefinite programming and geometric programming
- Numerical algorithms for smooth and equality constrained problems
- Interior-point methods for inequality constrained problems
- Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning and mechanical engineering
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