NTU Course
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Convex Optimization

Offered in 112-2
  • Serial Number

    16186

  • Course Number

    CommE5050

  • Course Identifier

    942 U0640

  • Class 01
  • 3 Credits
  • Elective

    GRADUATE INSTITUTE OF ELECTRICAL ENGINEERING / GRADUATE INSTITUTE OF ELECTRONICS ENGINEERING

      Elective
    • GRADUATE INSTITUTE OF ELECTRICAL ENGINEERING

    • GRADUATE INSTITUTE OF ELECTRONICS ENGINEERING

  • KUEN-YU TSAI
    • View Courses Offered by Instructor
    • COLLEGE OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE DEPARTMENT OF ELECTRICAL ENGINEERING

    • ktsai@ntu.edu.tw

    • R724, Minda bldg. (明達館724室)
    • 02-33663689

    • Admin. Assistance: Ms. Yi-Ru Chen (陳儀儒) 02-33669638 diochen@ntu.edu.tw
  • Thu 2, 3, 4
  • 電二101

  • Type 2

  • 25 Student Quota

    NTU 25

  • Specialization Program

    Signal Processing

  • English
  • NTU COOL
  • Core Capabilities and Curriculum Planning
  • Notes
    The course is conducted in English。
  • NTU Enrollment Status

    Enrolled
    0/25
    Other Depts
    0/0
    Remaining
    0
    Registered
    0
  • Course Description
    [Course description] Mathematical optimization has pervasive applications in not only almost all natural science and engineering disciplines such as electrical engineering (especially in control, communication, signal processing, and electronic design automation), computer science, and operations research, just to name a few, but also social sciences such as economics. Among various types of optimization problems, convex optimization problems are special in that they can be solved very efficiently, and thus they have gained much attention. Moreover, many optimization problems fall into this broad category. For instances, linear least squares, linear programming, quadratic programming, geometric programming, and semidefinite programming are special cases of convex optimization. The importance of convex optimization is becoming more and more apparent as there are many more emerging scientific and engineering problems being solved efficiently in this manner. This course primarily focuses on developing students’ capability of recognizing and formulating convex optimization problems arising from their own research fields, and when time permits, it also introduces how such problems are solved and applied. Students are also encouraged to develop heuristic approaches based on convex optimization theory and techniques to tackle general nonlinear, nonconvex optimization problems encountered in their fields of interest. [Course topics] 1. Introduction to convex optimization 2. Convex sets 3. Convex functions 3. Convex optimization problems 4. Duality theory (optimality conditions; sensitivity analysis) 5. Algorithms* (descent methods; Newton's method; interior-point methods) 6. Applications* (approximation and fitting, statistical estimation, etc.)
  • Course Objective
    [Course goals] Basic: - Recognize/formulate some engineering problems as convex optimization problems - Utilize or develop code to solve CVX optimization problems - Characterize optimal solution (e.g. limits of performance) Bonus: - Advance your own research work at NTU - Develop good presentation and technical writing skills in English - Develop heuristic approaches based on convex optimization to tackle general nonlinear, nonconvex optimization problems
  • Course Requirement
    [Prerequisites] Calculus (esp. Lagrange multiplier), linear algebra (esp. linear least squares and singular value decomposition)
  • Expected weekly study hours after class
  • Office Hour

    (appointments by email)

  • Designated Reading
    [BV04] S. Boyd and L. Vandenberghe, Convex Optimization
  • References
    [Ber99] D. P. Bertsekas, Nonlinear Programming, 2nd ed. [Ven01] P. Venkataraman, Applied Optimization with Matlab Programming  [BSS06] M. S. Bazaraa, M. D. Sherali, and C. M. Sherali, Nonlinear Programming, 3rd ed. [LY08] D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming
  • Grading
    0%

    Attendance

    0%

    Bonus Projects

    e.g., topical report/presentation, clarification of course material 20% max bonus.

    50%

    Final Project

    Proposal:Presentation:Report = 2:2:6; Format:Content = 1:1

    50%

    Final Exam

    Open books and notes. Maybe substituted with Course Study Report per instructor's decision.

    0%

    Homework

  • Adjustment methods for students
    Adjustment MethodDescription
    Teaching methods

    Assisted by video

    Exam methods

    Written (oral) reports replace exams

  • Course Schedule
    Week 1Course info. and Introduction
    Week 2
    Week 3Convex sets
    Week 4Convex functions
    Week 5Convex optimization problems
    Week 6Duality (I)
    Week 7
    Week 8Duality (II)
    Week 9
    Week 10Unconstrained minimization*; Equality-constrained minimization*
    Week 11Final project proposal presentation (Final project proposal due)
    Week 12Interior-point methods*
    Week 13Approximation and fitting*
    Week 14Statistical estimation*
    Week 15Geometric problems*
    Week 16Summary and Review; Techniques for Non-convex problems*
    Week 17Final exam
    Week 18Final project report/presentation 1st version due (present in class) (Final-exam week) 10% penalty/work day; last grade submission: 6/17