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
    Results are announced in obs.yildiz.edu.tr!

  • 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]
    Results are announced in obs.yildiz.edu.tr!

  • 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] [KKT Slide]

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

  • Week 14 (24.05.2024 at 10:00 in KMB-202): Research Seminar: Recent Results in Infinite-Dimensional Optimization
    [Slide] [Photo 1] [Photo 2]

Course Evaluation

  • Midterm: 35 %

  • Project: 25 %

  • Final: 40 %

Assignment Policy


All assignments will be announced at online.yildiz.edu.tr with a due date. Any assignment submitted after due date will be subject to a point deduction per given time interval.