CONVEX ANALYSIS AND OPTIMIZATION

Course Code:

MATH 355

Course Type:

Area Elective

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

7

Course Language:

English

Course Objectives:

This course is intended to introduce basic concepts of convex analysis and optimization theory. First the convex subsets and its geometric properties are defined. Then convex functions and functions of several variables are studied. Finally the convex optimization theory is discussed.

Course Content:

Affine subspaces, convex subsets, polyhedra, convex functions, differentiable functions of several variables, convex optimization theory

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) A sound understanding of convex subsets.	1,4,6	1	A,B
2) Learn the class of convex functions.	4,7	1	A,B
3) Learn differentiable functions of several variables.	2,4,7	1	A,B
4) Acquire knowledge of convex optimization theory.	1,2,4,7	1	A,B

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Fourier-Motzkin Elimination	Ch.1
2	Affine Subspaces	Ch.2
3	Convex Subsets	Ch.3
4	Polyhedra	Ch.4
5	Computations with polyhedra	Ch.5
6	Closed convex subsets and separating planes	Ch.6
7	Convex Functions	7.1, 7.2, 7.3, 7.4
8	Convex Functions	7.5, 7.6, 7.7, 7.8
9	Differentiable functions of several variables	8.1, 8.2
10	Differentiable functions of several variables	8.3, 8.4, 8.5
11	Convex functions of several variables	Ch.9
12	Convex optimization	10.1, 10.2, 10.3, 10.4
13	Convex optimization	10.5, 10.6, 10.7
14	Review

Recommended Sources

RECOMMENDED SOURCES
Textbook	Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker, Niels Lauritzen, World Scientific Publishing, Illustrated Edition.
Additional Resources

Material Sharing

MATERIAL SHARING
Documents
Assignments
Exams

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	25
Quizzes		-
Assignments	1	24
Total		49
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		51
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		49
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamental research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)					x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics					x
4	Ability to define, formulate and solve mathematical problems					x
5	Consciousness of professional ethics and responsibility			x
6	Ability to communicate actively			x
7	Ability of self-development in fields of interest				x
8	Ability to learn, choose and use necessary information technologies			x
9	Lifelong education			x

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	4	56
Hours for off-the-classroom study (Pre-study, practice)	14	6	84
Mid-terms (Including self-study)	1	15	15
Quizzes	-	-	0
Assignments	3	1	3
Final examination (Including self-study)	1	20	20
Total Work Load			178
Total Work Load / 25 (h)			7,12
ECTS Credit of the Course			7

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