Convex Optimization

This course concentrates on recognizing and solving convex optimization problems that arise in applications. The syllabus includes: convex sets, functions, and optimization problems; basics of convex analysis; least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems; optimality conditions, duality theory, theorems of alternative, and applications; interior-point methods; applications to signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design, and finance.

PREREQUISITES

You should have good knowledge of linear algebra and exposure to probability. Exposure to numerical computing, optimization, and application fields is helpful but not required; the applications will be kept basic and simple. You will use matlab and CVX to write simple scripts, so some basic familiarity with matlab is helpful. We will provide some basic Matlab tutorials.

INTENDED AUDIENCE

This course should benefit anyone who uses or will use scientific computing or optimization in engineering or related work (e.g., machine learning, finance). More specifically, people from the following fields: Electrical Engineering (especially areas like signal and image processing, communications, control, EDA & CAD); Aero & Astro (control, navigation, design), Mechanical & Civil Engineering (especially robotics, control, structural analysis, optimization, design); Computer Science (especially machine learning, robotics, computer graphics, algorithms & complexity, computational geometry); Operations Research; Scientific Computing and Computational Mathematics. The course may be useful to students and researchers in several other fields as well: Mathematics, Statistics, Finance, Economics.