ECE285, Fall 2026 – Semidefinite and Sum-of-squares Optimization(This is the Fall 2026 version of this course. For previous version, click here) Lectures: Tuesdays/Thursdays 12:30 pm -1:50 pm PST Location: Jacobs Hall (EBU1) Room 2315 Instructors:
Office hours:
Syllabus: ECE285 Course descriptionConvex optimization has profound impacts on many problems in control theory, discrete and nonlinear optimization, theoretical computer science, and machine learning. It is a fundamental tool to ensure efficient, resilient, and safe operations of many engineering systems, such as smart power grid, transportation, robotics, and many others. Optimization in these areas often takes the form of conic optimization, especially semidefinite programs. This course will cover semidefinite optimization which is a far-reaching generalization of linear programs. Another emphasis of the course will be on sum-of-squares optimization that deals with optimization problems involving polynomials. Some classical applications in control and recent ones in machine learning will be covered too. A tentative list of topics that we will cover includes
The students are expected to sign up on Piazza and GradeScope. Discussions and important announcements will happen on Piazza. The homework should be turned in and will be graded on GradeScope. Pre-requisitesThis course assumes basic knowledge in linear algebra. Some knowledge of convex optimization will be useful. Mathematical maturity, familiarity with MATLAB, Python, or similar software. Course grade
These weights are approximate; we reserve the right to change them later. The homework is carefully designed to develop genuine understanding of the material. Homework credit will count toward the course grade only if the midterm score is above 60%. Otherwise, the midterm score will be used for both the midterm and homework components. It is easy, and of little value, to appear knowledgeable. It is much harder, and far more valuable, to understand a topic precisely and communicate that understanding clearly. Working carefully through the homework problems is essential to developing this understanding for this course. Homework is submitted via Gradescope. The due date of each homework and project assignment will be clearly stated. We expect you to turn in all completed problem sets on time. No late homework will be accepted without prior approval. Approval is automatic the first three times you ask: you must email the instructor by midnight the day before (zhengy@ucsd.edu). Beginning with the second late homework, late homework will automatically lose 20% of the grade and no late homework will be accepted after 11:59pm two calendar days after the deadline. Collaboration policy: You are encouraged to work with other students on lecture notes, homework sets, general discussions of projects. But please note that the work you turn in should be your own! It is not acceptable to copy a solution that someone else has written. Instances of academic dishonesty will be referred to the Office of Student Conduct for adjudication. SoftwareYou will use one of YALMIP (Matlab), CVX (Matlab), CVXPY (Python) or CVXOPT (Python), to write simple scripts for homework questions. AI usage policyGenerative AI tools (such as ChatGPT and Claude etc.) are becoming more widely available and can be valuable resources when used thoughtfully and responsibly. In this course, you are permitted to use generative AI tools to brainstorm ideas, clarify complex concepts, organize your thoughts, and check grammar of your writing. However, you must write your own solutions in the end. It is academically dishonest and unacceptable to submit any work generated by an AI as your own. The core principle is that the work you submit must reflect your own understanding and intellectual effort. You should be able to explain the reasoning behind every step of your submitted work. If you use an AI tool for assistance in any assignment, I would appreciate a brief statement at the end of your work clarifying which tool you used and for what specific purpose. Submitting AI-generated content without proper attribution or presenting it as your own original work constitutes a violation of academic integrity. You are responsible for the factual accuracy and originality of everything you submit. If you are unsure whether a particular use is acceptable, please ask before submitting your work. References
Academic IntegrityUCSD's Code of Academic Integrity applies to this course. It is dishonest to cheat on exams, copy other people's work, or fake experimental results. An important element of academic integrity is fully and correctly acknowledging any materials taken from the work of others. Instances of academic dishonesty will be referred to the Office of Student Conduct for adjudication. AcknowledgmentsThe initial development of this course was inspired by the following courses:
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