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Syllabus ( IE 612 )

   Basic information
Course title: Introduction to Convex Optimization
Course code: IE 612
Lecturer: Assist. Prof. Figen ÖZTOPRAK TOPKAYA
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 1/2, Fall and Spring
Level of course: Third Cycle (Doctoral)
Type of course: Area Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: NONE
Professional practice: No
Purpose of the course: Convex optimization problems arise in several engineering applications. This course aims at providing an introduction to convex optimization by discussions on selected convex programming problems. In this regard, the course covers the relevant mathematical background, basic theory, numerical algorithms, and some applications of those problems.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Ability to identify convex analysis

    Contribution to Program Outcomes

    1. Ability to define Industrial Engineering problems in complex industrial systems and processes, offer innovative designs or solutions to improve performance dimensions
    2. Ability to deepen at the level of expertise in the field of Industrial Engineering by using the knowledge gained at the undergraduate and graduate level and by reaching and comprehending the latest information

    Method of assessment

    1. Written exam
    2. Homework assignment
    3. Term paper
  2. List Karush–Kuhn–Tucker conditions, Identify duality and the impact on optimization approaches

    Contribution to Program Outcomes

    1. Ability to define Industrial Engineering problems in complex industrial systems and processes, offer innovative designs or solutions to improve performance dimensions
    2. Ability to do comprehensive research that bring innovation to science or technology, develop a new scientific method/design or technological product/process, or apply a known method to a new field
    3. Ability to deepen at the level of expertise in the field of Industrial Engineering by using the knowledge gained at the undergraduate and graduate level and by reaching and comprehending the latest information

    Method of assessment

    1. Written exam
    2. Homework assignment
    3. Term paper
  3. To identify and use conic programming practices and conical duality

    Contribution to Program Outcomes

    1. Ability to define Industrial Engineering problems in complex industrial systems and processes, offer innovative designs or solutions to improve performance dimensions
    2. Ability to deepen at the level of expertise in the field of Industrial Engineering by using the knowledge gained at the undergraduate and graduate level and by reaching and comprehending the latest information

    Method of assessment

    1. Written exam
    2. Homework assignment
    3. Term paper
  4. Implement semi-definite programming

    Contribution to Program Outcomes

    1. Ability to define Industrial Engineering problems in complex industrial systems and processes, offer innovative designs or solutions to improve performance dimensions
    2. Contribute to the solution of social, scientific, cultural and ethical problems encountered in the field of Industrial Engineering and business life
    3. Ability to deepen at the level of expertise in the field of Industrial Engineering by using the knowledge gained at the undergraduate and graduate level and by reaching and comprehending the latest information

    Method of assessment

    1. Written exam
    2. Homework assignment
    3. Term paper
  5. To be able to identify the solution methods and choose the most suitable method for the problem.

    Contribution to Program Outcomes

    1. Ability to define Industrial Engineering problems in complex industrial systems and processes, offer innovative designs or solutions to improve performance dimensions
    2. Contribute to the solution of social, scientific, cultural and ethical problems encountered in the field of Industrial Engineering and business life
    3. Ability to deepen at the level of expertise in the field of Industrial Engineering by using the knowledge gained at the undergraduate and graduate level and by reaching and comprehending the latest information

    Method of assessment

    1. Written exam
    2. Homework assignment
    3. Term paper
   Contents Up
Week 1: What is convex optimization? Convex functions and their properties
Week 2: Examples of convex optimization problems
Week 3: Some applications of convex programming
Week 4: The dual of a convex program and optimality conditions, Homework 1
Week 5: Conic quadratic programming - mathematical background
Week 6: Conic quadratic programming - applications
Week 7: Conic programming - conic duality, Homework 2
Week 8: Conic programming - conic duality - Midterm Exam
Week 9: Semidefinite programming - mathematical background, Project 1 Submission
Week 10: Semi-definite programming - implementation
Week 11: An overview of solution algorithms, Homework 3
Week 12: Interior point method - construction of the classical algorithm, Project 2 Submission
Week 13: Primal-dual interior point algorithms
Week 14: Modern convex optimization solvers
Week 15*: -
Week 16*: Final Exam
Textbooks and materials: Lectures on Modern Convex Optimization, A. Ben Tal and A.Nemirovski, MOS-SIAM Series on Optimization, 2001.
Recommended readings: Convex Optimization, S.Boyd and L.Vandenberghe, Cambridge University Press, 2004.
Introductory Lectures on Convex Optimization: A Basic Course, Y. Nesterov, Springer, 2003.
Convex Analysis and Nonlinear Optimization, J.Borwein and A.Lewis, Springer, 2005.
Convexity, Duality, and Lagrange Multipliers, D.Bertsekas, A.Nedic, and A.Ozdaglar, Lecture Notes, MIT, 2011.
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 35
Other in-term studies: 0
Project: 9,12 15
Homework: 4,7,11 10
Quiz: 0
Final exam: 16 40
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 6 3
Term project: 6 8
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 2 1
Personal studies for final exam: 10 1
Final exam: 3 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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