# Department of Electrical and Electronics Engineering

Course Details

#### ELE704 - Optimization

2022-2023 Fall term information
The course is not open this term
ELE704 - Optimization
 Program Theoretıcal hours Practical hours Local credit ECTS credit PhD 3 0 3 10
 Obligation : Elective Prerequisite courses : - Concurrent courses : - Delivery modes : Face-to-Face Learning and teaching strategies : Lecture, Question and Answer, Problem Solving Course objective : It is aimed to give the following topics to the students; a) Recognising and classifying an optimisation problem, b) Tools for learning and analysing convex sets and functions, c) Basic algorithms used in solving convex optimisation problems, d) Duality concept in constrained problems and the techniques being used to apply them, mainly staying in the context of convex optimisation, so that they can solve problems which they may encounter with in their studies/projects. Learning outcomes : Recognise and classify optimisation problems Model the problem s/he encounters with as an optimisation problem Know which algorithms can s/he use to solve the problem s/he established, know the advantages and disadvantages of these algorithms Apply the techniques and algorithms s/he learnt in the class to her/his thesis studies and also real-life applications Have the adequate knowledge to follow and understand advanced up-to-date optimisation algorithms Course content : Brief reminder of linear algebra topics, Convexity, convex sets and functions, Gradiant Descent, Steepest Descent, Newton Algorithms and their variations for unconstrained problems, Constrained problems and Karush-Kuhn-Tucker Conditions, Modification of the above algorithms for unconstrained problems to constrained problems, İnterior Point Algorithms (Penalty ve Barrier Methods) References : 1. Luenberger, Linear and Nonlinear Programming, Kluwer, 2002.; 2. Boyd and Vandenberghe, Convex Optimization, Cambridge, 2004.; 3. Baldick, Applied Optimization, Cambridge, 2006.; 4. Freund, Lecture Notes, MIT.; 5. Bertsekas, Lecture Notes, MIT.; 6. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.
Course Outline Weekly
Weeks Topics
1 Brief reminder of linear algebra topics
2 Brief reminder of linear algebra topics
3 Optimality conditions for unconstrained problems Convex Sets
4 Convex and concave functions Conditions for convexity Operations that preserve convexity
5 Quadratic functions, forms and optimization Optimality conditions Unconstrained minimization
6 Descent Methods Convergence
8 Algorithms: Steepest Descent Algorithm
9 Algorithms: Newton?s Algorithm
10 Midterm Exam
11 Constrained optimization Duality
12 Optimality conditions, KKT Conditions Algorithms: Feasible Direction Method, Active Set Method
13 Algorithms: Gradient Projection Method, Newton?s Algorithm with Equality Constraints
14 Algorithms: Penalty and Barrier Methods
15 Study week
16 Final Exam
Assessment Methods
Course activities Number Percentage
Attendance 0 0
Laboratory 0 0
Application 0 0
Field activities 0 0
Specific practical training 0 0
Assignments 13 30
Presentation 0 0
Project 0 0
Seminar 0 0
Quiz 0 0
Midterms 1 30
Final exam 1 40
Total 100
Percentage of semester activities contributing grade success 60
Percentage of final exam contributing grade success 40
Total 100
Course activities Number Duration (hours) Total workload
Course Duration 14 3 42
Laboratory 0 0 0
Application 0 0 0
Specific practical training 0 0 0
Field activities 0 0 0
Study Hours Out of Class (Preliminary work, reinforcement, etc.) 14 3 42
Presentation / Seminar Preparation 0 0 0
Project 0 0 0
Homework assignment 13 5 65
Quiz 0 0 0
Midterms (Study duration) 1 25 25
Final Exam (Study duration) 1 30 30