ECE 273
Convex Optimization and Applications

Spring 2015




Practical Information

Course load

4 units

Lectures

Wednesday 5:00-7:50pm and 8:30-9:50pm, WLH 2111

Instructor

Gert Lanckriet

Email: gert@ece.ucsd.edu
Office: 5604 Jacobs Hall
Office hours: Tuesday 3:30-3:55pm / Wednesday 3:45-4:50pm

TA

Ning Ma
Email: nima@eng.ucsd.edu
Office: Jacobs Hall, Room 2321
Office hours: Monday 12:00PM - 1:30PM, Friday 10:50AM - 11:50AM, 4:00PM - 5:00PM.

Grading

Homework: 20%
Midterm: 50%
Project: 30%

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Updates and Announcements

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Course Description

Convex optimization relates to a class of nonlinear optimization problems where the objective to be minimized and the constraints are both convex. Convex optimization problems are attractive because a large class of these problems can now be efficiently solved. However, the difficulty is often to recognize convexity: convexity is harder to recognize than say, linearity. Moreover, it is possible to address certain hard, non-convex problems (combinatorial optimization, integer programming) using convex approximations that are more efficient than classical linear ones. This course covers some convex optimization theory and algorithms, and will concentrate on formulating/recognizing and solving convex optimization problems in applications arising in a variety of field (e.g., analysis, design and control of complex systems, machine learning, applied statistics, financial engineering, communication theory, signal processing, circuit design, combinatorial optimization, computational geometry, computational biology and mechanical engineering).

Objectives

Intended Audience

Students interested in scientific and engineering problems where optimization plays a role. Related departments/fields include: bioengineering, civil and environmental engineering, electrical engineering (signal and image processing, control and communications, robotics, CAD), computer science (computer graphics, artificial intelligence and decision theory, data mining, algorithms & complexity, computational geometry), industrial engineering and operations research, mechanical and structure engineering (robotics, control, structural analysis, optimization and design), scientific computing and computational mathematics, statistics (model fitting and selection; experimental design), finance, economics.

Outline

Theory Algorithms Applications

Required background

Basic linear algebra (matrices, eigenvectors, symmetric matrices, positive-definite matrices). Prior exposure to optimization (e.g., linear programming) helps but is not necessary.

Textbook and optional references

The textbook for this course is Convex Optimization (S. Boyd & L. Vandenberghe, Cambridge University Press 2004). The book is available online at http://www.stanford.edu/~boyd/cvxbook/ or at http://www.ee.ucla.edu/~vandenbe/cvxbook/.

Other useful references: Back

Homework

Homework is assigned every other week and due the following week. You are allowed, even encouraged, to work on the homework in small groups, but you must write up your own homework to hand in. Indicate with whom you discussed homework problems. Late homework will not be accepted.

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Midterm

A midterm will be held in class on 05/27/15. The midterm is closed-book but you are permitted to bring in one page of notes (letter size, both front and back allowed, hand-written).

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Project

There will be a project instead of a final, involving independent work on a topic of choice. You are welcome to choose a project that intersects with your current research interests. Back

Software

Here are a couple of Matlab tutorials that you might find helpful: http://www.math.ufl.edu/help/matlab-tutorial/ and http://www.math.mtu.edu/~msgocken/intro/node1.html. There are various types of publicly-available packages that may be useful to you: Back