This course focuses on the basics of optimization theories and applications. The first part of the course will be mainly about linear optimization, including how to formulate a linear program, the simplex method and the duality theory. Then we will study nonlinear optimization, focusing on the optimality conditions and some useful algorithms. Integer programming will also be briefly discussed in this course.

Teaching Team

Instructor
Junfeng Wu

TA
Junhu Jin, Haoying Li, Ziwei Zhu, Jianting Pan, Runze You, Rongsen Jin

Logistics

  • Lectures 03: are on Monday/Wednesday 10:30AM - 11:50AM in Cheng Dao 101.
  • Parallel sessions (Session 1 and 2) are introduced by Prof. Shi Pu.
  • Office hours
    • Junfeng Wu: Mon 4:30-5:30 PM. Daoyuan Building 402
    • Junhu Jin: TUE 2:00-3:00 PM. SDS Research Lab (4th Floor, Zhi Xin Building)
    • Ziwei Zhu: TUE 9:00-10:00 AM. SDS Research Lab (4th Floor, Zhi Xin Building)
    • Haoying Li: TUE 3:00-4:00 PM. SDS Research Lab (4th Floor, Zhi Xin Building)
    • Jianting Pan: TUE 10:00-11:00 AM. SDS Research Lab (4th Floor, Zhi Xin Building)
    • Runze You: Wed 9:20-10:20 AM. Daoyuan building, 224
    • Rongsen Jin: Mon 9:00-10:00 AM. Tu Huilong building, 312
  • Contact: If you have any question, please reach out to us via email or post it to BB.

Course Information

Reference Books

  • "Introduction to Linear Optimization", by D. Bertsimas and J. Tsitsiklis
  • "Convex Optimization", by S. Boyd and L. Vandenberghe (electronic copy available online)
  • " Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with MATLAB", by A. Beck

    • Grading Policy (MAT3007)

    Assignments (20%)

    Midterm exam (40%)

    Final exam (40%)

    Schedule

    Week Topics Lecture Notes Tutorials Homework
    1 Introduction to optimization [Slides1]
    [Slides2]
    2-4 Basics about linear optimization, the simplex algorithm [Slides3]
    [Slides4]
    [Slides5]
    [Slides6]
    [Slides7]
    [Slides8]
    [Slides9]
    [Slides10]
    		 [Tutorial1]
    [Tutorial2]
    [Tutorial3]
    		 [Homework1]
    [Homework2]
    4-5 Duality theories of linear programs [Slides11]
    [Slides12]
    		 [Tutorial4]
    [Tutorial5]
    		 [Homework3]
    6 Dual simplex, sensitivity analysis and more on LP [Slides13]
    [Slides14]
    [Slides15]
    		 [Tutorial6]
    		 [Homework4]
    7 Review and midterm [Slides16]
    8-10 Introduction to nonlinear optimization, optimality conditions [Slides17]
    [Slides18]
    [Slides19]
    [Slides20]
    [Slides21]
    [Slides22]
    		 [Tutorial7]
    [Tutorial8]
    [Tutorial9]
    		 [Homework5]
    [Homework6]
    11-12 Algorithms for nonlinear optimization [Slides23]
    [Slides24]
    [Slides25]
    [Slides26]
    		 [Tutorial10]
    [Tutorial11]
    		 [Homework7]
    [Homework8]
    13-14 Integer programs, introductions and basic algorithms, and final review [Slides27]
    [Final Review]
    		 [Tutorial12]
    		 [Homework9]