## 22494 Convex Optimization: Course Information## LecturesLectures are Sundays and Tuesdays, 9:00–10:30 am, via webinar. Click here to learn more about our webinars. ## Office hours
Artin Tajdini: Wednesdays, 2:00–3:00 pm, via webinar Parsa Mashayekhi: Tuesdays, 3:00–4:00 pm, via webinar Mojtaba Zare: Mondays, 3:00–4:00 pm, via webinar
## Textbook and optional referencesThe course materials are the same as EE364a (Stanford) and EE236b (UCLA). Specifically, the textbook and lecture slides can be found here. ## Course requirements and grading**Requirements:***Weekly homework assignments*, due each Friday 5pm, starting February 21. You are allowed, even encouraged, to work on the homework in small groups, but you must write up your own homework to hand in. Each question on the homework will be graded on a scale of {0, 1, 2}. Some assignments require you to use convex programming software such as CVX (Matlab), CVXPY (Python), Convex.jl (Julia), or CVXR (R), which we refer to as CVX*.*Midterm quiz*. The format is an in-class, 75 minute, closed book, closed notes midterm scheduled for Sunday April 5.*Final exam*. The format is a 24 hour take home, scheduled for the last week of classes, nominally Sunday June 28–29.
**Grading:**Homework 20%, midterm 10%, final exam 70%. These weights are approximate; we reserve the right to change them later.
*Update*. The final weights are the solution of the following linear program
\[ \begin{array}{ll} \mbox{maximize} & c^Tx + (2-a)\max(c_{Quera/Lecture}, c_{Homework}) + c_{ExtraCreditProblem}\\ \mbox{subject to} & 1^Tx = 1^T\tilde{x} \\ & \dfrac{1}{a} \leq \dfrac{x_i}{\tilde{x}_i}, \quad 1\leq i\leq 3\\ & 0 < a \leq 0.3\big(\prod_{i=1}^3 x_i\big)^{\frac{1}{3}}. \end{array} \] Note that the coefficient \(2-a\) will never be negative, as we have: \[ a \leq 0.3\big(\prod_{i=1}^3 x_i\big)^{\frac{1}{3}} \leq 0.3 \big(\dfrac{\sum_{i=1}^3 x_i}{3}\big) = 0.3 \big(\dfrac{\sum_{i=1}^3 \tilde{x}_i}{3}\big) = 0.3 \big(\frac{20}{3}\big) = 2 \]
## PrerequisitesGood knowledge of linear algebra (as in 22255), and exposure to probability. Exposure to numerical computing, optimization, and application fields helpful but not required; the applications will be kept basic and simple. ## QuizzesThis class has ## Catalog descriptionConcentrates on recognizing and solving convex optimization problems that arise in applications. 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. ## Course objectivesto give students the tools and training to recognize convex optimization problems that arise in applications to present the basic theory of such problems, concentrating on results that are useful in computation to give students a thorough understanding of how such problems are solved, and some experience in solving them to give students the background required to use the methods in their own research work or applications
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