MS&E310 (Conic) Linear Optimization 2023-2024 Autumn

| Announcements (Updated Frequently) | General Info | Course Info | Handouts | Assignments |

• Class Times and Locations
  • Lectures: MoWe 11:30AM - 1:00PM.
  • Lecture Room: McCullough 122.
  • Extra Session (Discussion, Make-Up Lectures): Friday 11:30-1:00pm (same room), https://stanford.zoom.us/my/yinyuye (password would be sent by e-mail)

• Prerequisites : Math 113 or equivalent (Math 115 is recommended).

• Text: Linear and Nonlinear Programming, 5th Edition, Springer, by Luenberger and Ye. All other lecture notes will be distributed via the course website. Also check CLP monograph
  and for Various Matlab Solvers, such as hsdLPsolver.m
  
  

Course Staff

• Professor: Yinyu Ye
  • Office hours: Tuesdays 2:30 - 3:30pm (Check the announcement site for any possible change), or by appointment
  • Email: yinyu-ye@stanford.edu
  • Phone: 723-7262
  • Office: Huang 308 and https://stanford.zoom.us/my/yinyuye
• Course Assistant: ?
  • Office: ?
    
  • Office hours: ?
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• Staff Support: Jackie Nguyen
  • Office: Huang
  • Email: jackie.nguyen@stanford.edu
  • Phone:

Grading and Exams

Your grade in this course would be based on a take-home midterm exam and a teacm project.

• Homework Exercises: not be graded but discussed in problem sessions;
• Midterm exam: November 3-5 take home, 50%;
• A project (up to two students): report due December 11 50%.

Topics include: Problem formulation of standard (conic) linear programming models, the theory of polyhedral and conic convex sets, linear inequali­ties, alternative theorems and conic duality, sensitivity analyses and economic interpretations, and relaxations of harder optimi­zation problems. Algorithms include the simplex method, interior-point methods, first-order methods, and ADMM and other customized iterative methods. Complexity and/or computation efficiency analysis for conic linear programming. Applications of this year include: Online Linear Programming, Dynamic and Online Pricing/Resource-Allocation, SVM and Data Classification, Markov Decision Process and Reinforcement Learning, Data Wassestein Berry Center via Optimal Transport, Sensor-Network Localization, Max-Cut and Bisection Relaxations, Algorithmic Game Equilibrium, Core of Games, Distributionally Robust Decisioning and Learning, Financial Techniques and Risk Management, Sparse and Low Rank Regression,... .
The field of optimization is concerned with the study of maximization and minimization of mathematical functions. Very often the arguments of (i.e., variables in) these functions are subject to side conditions or constraints. By virtue of its great utility in such diverse areas as applied science, engineering, economics, finance, medicine, and statistics, optimization holds an important place in the practical world and the scientific world. Indeed, as far back as the Eighteenth Century, the famous Swiss mathematician and physicist Leonhard Euler (1707-1783) proclaimed that ... nothing at all takes place in the Universe in which some rule of maximum or minimum does not appear. The subject is so pervasive that we even find some optimization terms in our everyday language.
Linear Optimization is so large a subject that it cannot adequately be treated in the short amount time available in one quarter of an academic year. In this course, we shall restrict our attention mainly to some aspects of linear optimization, such as model formulation, duality theories, and algorithm complexities.
Linear Optimization often goes by the name Linear Programming (LP). The word "Programming" should not be confused with computer programming which in fact it antedates. As originally used, the term refers to the timing and magnitude of actions to be carried out so as to achieve a goal in the best possible way. Linear Programming is one of the central quantitative decision models in Management Science and Operations Research. Highlights of this year's topics are Economic pricing, compressed sensing, on-line linear programming, core of game, financial Decision and risk management, dynamic resource allocation, and their computations, which you would learn during the process of the course.