Stanford EE364A Convex Optimization I Stephen Boyd I 2023 I Lecture 1

Course Logistics

• The course will primarily use Ed, with a static course website as a supplement.
• Contact the staff using the provided email address, which goes to all TAs.
• Course requirements include weekly homework assignments, a midterm quiz, and a 24-hour take-home final exam.

Course Content

First Three Weeks

• The initial focus will be on math, which may be challenging for those more interested in applications.
• Topics will include basic concepts like declining verbs in Spanish and pronouncing tones in Chinese.
• The midterm quiz will cover material from these first three weeks and will be in a traditional format, focusing on basic material without gratuitous math.

Transition to Applications

• After the first three weeks, the course will transition to applications, making the material more relevant and interesting.
• Python and CVX Pi will be the primary tools, with support for other languages like CVX R, CVX JL, and CVX MATLAB.

Prerequisites

• Prerequisites include linear algebra, probability, and basic Python skills.

Chat GPT and Language Models

• Chat GPT has been used to generate solutions to homework and final exam problems, but its responses are often incorrect despite being well-written.
• The instructors plan to train a large language model using the discussion forum to provide accurate answers to students' questions.

Optimization Basics

Introduction

• Optimization problems involve choosing decision variables to minimize an objective function while satisfying constraints.
• The objective function represents the best effort, and the smaller or more negative its value, the better.
• Constraints are predicates that evaluate to true or false and describe limitations or preferences.
• A solution or optimal point (xstar) has the smallest objective value among all choices that satisfy the constraints.

Examples

• Portfolio optimization: Construct a portfolio with minimum risk while meeting various constraints.
• Device sizing in electronic circuits: Determine the size of gates to meet timing requirements while considering factors like area and power consumption.

Applications

• Circuit design: Size critical paths to ensure signal validity.
• Data fitting: Find parameters in a model that minimize misfit with training data while promoting robustness.

Convex Optimization

• Convex optimization is a mathematical technique used to solve optimization problems with non-negative curvature.
• Linear programming is a specific type of convex optimization problem with analytical solutions for a limited number of cases.
• Convex optimization problems are ubiquitous in various fields, including supply chain management, scheduling, and engineering.
• Recognizing convex functions is crucial for solving convex optimization problems, and the course will focus on developing this skill.

Course Structure and Expectations

• The course aims to train students to recognize and solve convex optimization problems.
• Students will gain practical experience by writing 10-line scripts and working on problems in various fields.
• The focus is on solving problems rather than delving into the theory behind optimization.
• The course will provide a sandbox environment for students to practice and master various optimization techniques.
• The tone of the course will change significantly after the first class, becoming more challenging and in-depth.