Short Course: Convex Optimization with Engineering Applications

  This course will provide students with mathematical tools and training to deal with optimization problems in engineering. It will introduce basic convex optimization models and robust optimization techniques. All concepts and theories will be illustrated with numerous applications from signal processing, digital communication (wireless communication system design), control, and circuit design. A main objective is to teach students how to give good and robust formulations to engineering problems in a way that is amenable to effcient solution by modern optimization algorithms. This course is intended to provide a core optimization background for undergraduate/graduate students from such areas like applied mathematics, signal and image processing, communications, control, CAD, robotics, structural analysis, computer graphics, algorithms & complexity, computational geometry.

  Recommended Reference: 1. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press. 2. D. Bertsekas, Nonlinear Programming. Athena Scienti¯c. Prerequisites: Mathematical maturity, comfortable with linear algebra, probability theory, analysis. Exposure to Matlab, numerical optimization, and application ¯elds helpful but not required. Tentative Course Outline: 1. Lecture 1: Introduction, convex sets and functions 2. Lecture 2: Convex optimization problems and interior point methods 3. Lecture 3: Robust optimization: complexity and approximations, applications to robust beamforming, linear estimation



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