MTM4502 – Optimization Techniques (Spring 2023-2024)

Instructor Information

• Instructors: Gökhan Göksu (Gr. 2) and Hale Gonce Köçken (Gr. 4)

• E-mail (GG): gokhan [dot] goksu [at] yildiz [dot] edu [dot] tr

• E-mail (HGK): hgonce [at] yildiz [dot] edu [dot] tr

General Information

• Schedule: Friday, 09:00-12:00

• Classroom: KMB-224

• Office Hours: Friday, 14:00-17:00 (and/or by appointment)

Expectations and Goals

• Establishment of mathematical models that provide optimal decision making, demonstration of real-life application areas and application of solution methods.

Course Materials

• Textbook:

  • E. K. Chong and S. H. Zak (2013). An Introduction to Optimization (Vol. 76). John Wiley and Sons.

• Optional Materials:

  • S. Boyd and L. Vandenberghe (2004). Convex Optimization. Cambridge University Press.

  • M. A. Bhatti (2000). Practical Optimization Methods with Mathematica Applications, Springer-Verlag New York.

  • R. Fletcher (1987). Practical Methods of Optimization, Second Edition, John-Wiley and Sons Ltd., Chichester, New York.

Tentative Course Schedule

• Week 1 (23.02.2024): Introduction, Basic Concepts
  [Slide]

• Week 2 (01.03.2024): Gradient, Hessian Matrix, Definiteness of a Matrix, Convexity of Functions
  [Slide]

• Week 3 (08.03.2024): Convexity of Functions (continued), Constrained and Unconstrained Optimization: Local and Global Minimum, Set of Feasible Directions, Necessary and Sufficient Conditions for Local Minimum
  [Slide]

• Week 4 (15.03.2024): Practical Problems in Unconstrained Optimization (Slides of Last Week), Iterative Methods in Unconstrained Optimization, Gradient Methods: Steepest Descent Method
  [Slide]

• Week 5 (22.03.2024): Steepest Descent Method for a Quadratic Function
  [Slides of Last Week]

• Week 6 (29.03.2024): Newton's Method for Multivariable Functions, Conjugate Direction Methods and Algorithms
  [Slide]

• Week 7 (05.04.2024): Review
  [In Class Materials]

• Week 8 (12.04.2024): No Class (Eid al-Fitr)
  [No Class]

• Week 9 (19.04.2024, 14:00-16:00): Midterm Exam
  [Midterm]

• Week 10 (26.04.2024): MATLAB Tutorial Session I: Iterative Methods in Unconstrained Optimization
  [MATLAB Tutorial Session I] [MATLAB Tutorial Session GitHub Page] [Project Assignment]

• Week 11 (03.05.2024): Constrained Optimization: Problems with Equality Constraints, Lagrange Multipliers
  [Slide]

• Week 12 (10.05.2024): Constrained Optimization with Equality and Inequality Constraints: Karush-Kuhn-Tucker Conditions, Constrained and Unconstrained Optimization under Nonnegativity Constraints
  [Slide]

• Week 13 (17.05.2024): MATLAB Tutorial Session II: Problems with Equality Constraints
  [MATLAB Tutorial Session II]

• Week 14 (24.05.2024): TBA
  [Slide]

Course Evaluation

• Midterm: 35 %

• Project: 25 %

• Final: 40 %

Assignment Policy