Probability Theory and Stochastic Processes, Linear Algebra, Mathematical analysis and Matlab programming.
Upon successful completion of this course, the students should:
have acquired the mentality and language of optimization.
know how to recognize, model and formulate real engineering problems as optimization problems.
understand the underlying theory, concepts and properties related to each of the optimization tools, especially those that are useful for computing solutions efficiently in convex optimization problems.
be able to design, implement and simulate practical algorithms to solve the various optimization problems.
be able to analyze the structures of problems and associated solutions, as well as the relationships between different problems.
The focus of the course is to provide in depth study of convex optimization tools in the context of important problems related to various engineering applications. On the one hand, these are very useful tools in order to understand, model and analyze correctly real problems, and on the other hand, these are also the key tools to design optimal or close-to-optimal solutions for these problems. The course covers the following topics: convex sets and convex functions, linear and quadratic programming, semi-definite programming, duality, Pareto optimization, first-order and second-order iterative optimization algorithms, interior-point methods. The various optimization techniques will be continuously illustrated to solve important engineering problems in different areas, such as approximation and fitting, statistical signal processing, classification, problems on graphs and communication networks, control, computational geometry, data analytics, machine learning, task scheduling and portfolio optimization.
Lectures, homework exercises, self-study.
Compulsory attendance is the only requirement.
Assessment methods and criteria
Either a Final Take-home Exam or a Project work (student choice).
The Final Grade: pass (A or B) or fail (based on 30% of homework grade + 70% of final examination/project grade).