Undergraduate Teaching:

Fall 2012: EE362K -- Introduction to Automatic Control

    This class is about understanding how to analyze and design feedback systems. Feedback sytems are all around us, from the local and global economy, the response of the electricity grid to additional load or supply, the suspension in our car or the cooling of our thermostat, to more complicated biological processes. The structure of this class marks a departure from classical or more traditional presentations of the material, in that there is a great emphasis on state space concepts and tools. Important and intuitive concepts, typically reserved for advanced classes, are presented here, including observability and reachability, as well as some basics of nonlinear systems (in particular, linearization, and basic Lyapunov stability). There is a very large emphasis on linear algebra, from the linear operator and matrix algebra perspectives.

Graduate Teaching:

Fall 2012 - Spring 2013: EE381V -- Large Scale Optimization and Learning

    This is a new class co-taught by Prof. Sujay Sanghavi and myself. The last few years have seen tremendous attention in research, various sectors of industry (including startups), the media, etc., to problems in machine learning, in particular, problems in BIGDATA – including problems exhibiting an inherent high dimensionality, and problems involving truly massive data sets.

New ideas are required on two fronts: On the probability / statistics side, we have to rethink what kind of patterns we can find, what consistency and statistical reliability mean, what resilience to noise and corruption entails, etc., in such settings. On the algorithmic side, such massive problems require different computational approaches. In particular, interior point methods, SDP solvers, etc., that were the golden child of optimization in the last two decades, no longer seem appropriate in this new important context.

The philosophy and thus aim of both parts of this course will be to accomplish a judicious mix of theory and application: we will develop results in a rigorous way, proving key steps along the way, but homeworks will have a heavy computational element, featuring a series of what amounts to computational projects, requiring working with non-toy‐size problems in Matlab.

Fall 2012 Course web page.

Fall 2010/2013: EE380K -- System Theory and Control

    This class is one of the core CommNetS classes, and it serves as an introduction to concepts and tools from system theory. It covers: Advanced linear algebra, including matrix algebra and analysis, and theory of linear operators. The first part of the course is primarily concerned with developing these important tools. It forms the technical bulk of the class, and developing this direction is as much a focus and goal of the course as anything else. Then, we cover basics of linear systems in the time domain, including solution to LTI systems, Lyapunov equations and stability, reachability/observability. Finally, we introduce the basics of optimal control, including the principle of optimality and the HJB equation. We consider the LQR and Riccatti equations in detail. In the process, topics like Semidefinite matrices are explored.

Fall 2009/2011: EE381V-11 -- Convex Analysis: Optimization, Algorithms and Applications

    This is an research-level graduate class geared towards advanced graduate students. The topics change from year to year, to reflect latest developments in the field, exciting topics, and topics of most interest (to me, and hopefully to graduate students as well!). In the past two offerings, the first half of the course has focused on Convex Analysis, developing the geometry of convexity and proving the basic duality results of convex sets and then convex functions. The goal is to impart an appreciation of the questions, tools, and techniques central to convex analysis, to enable the student to go on to read the foundational texts on the topic. After this, the course then considers advanced special topics in optimization. In the past, this list has included: Moment problems and sum of squares polynomials, applications of Semidefinite optimization, Robust optimization and applications, combinatorial optimization.

In Fall 2011, the focus will switch to applications of Convex Analysis and Optimization to advanced topics in Statistics, particularly in High Dimensional Statistics. Check back here later in the Spring term (2011) for further details.