YAŞAR UNIVERSITY
SCIENCE AND LETTERS FACULTY
MATHEMATICS DEPARTMENT
COURSE SYLLABUS
Course
Code
Semester
Math 451
Fall
Course Title
Convex Analysis and Optimization
Course Hour/Week
Theory
3
Practice
0
Yaşar Credit
ECTS
3
5
Course Type
1. Compulsory Courses
1.1. Programme Compulsory Courses
X
1.2. University Compulsory Courses (UFND)
1.3. YÖK (Higher Education Council) Compulsory Courses
2. Elective Courses
2.1. Program Elective Courses
2.2. University Elective Courses
3. Prerequisites Courses
3.1. Compulsory Prerequisites Courses
3.2. Elective Prerequisites Courses
Language of Instruction
English
Level of Course
Undergraduate (First Cycle)
Prerequisites Course(s) (compulsory)
-
Special Pre-Conditions of the Course
(recommended)
-
Course Coordinator
Assoc. Prof., Şahlar Meherrem
Course Instructor(s)
Assoc..Prof., .Şahlar Meherremv
Mail: sahlar.meherrem@yasar.edu.tr
Web:smaharramov.yasar.edu.tr
Mail: sahlar.meherrem@yasar.edu.tr
Web: smaharramov.yasar.edu.tr
Course Assistant(s)/Tutor (s)
Aim(s) of the Course
Mathematics is both an art and a science, and pure mathematics lies at its
heart. Pure mathematics explores the boundary of mathematics and pure
reason. It has been described as "that part of mathematical activity that is
done without explicit or immediate consideration of direct application,"
although what is "pure" in one era often becomes applied later. Optimization
and optimal control processes are current examples of areas to which pure
mathematics is applied in significant ways.
The following courses are designed for students who want to study topics in
applied mathematics at a less intensive level than the applied math major
courses which prepare students for graduate school
Learning Outcomes of the Course
Course Content
COURSE OUTLINE/SCHEDULE (Weekly)
Preliminary Preparation
Week
Topics
Methodology and
Implementation
(theory, pratice,
assignment etc.)
Convex sets and Convex Functions
Jonathan M. Borwein and Adrian
S.Lewis, Convex Analysis and
Nonlinear Optimization, Theory
and Examples, Springer 2000
Chapter1
Theory and Practice
Optimality conditions
Jonathan M. Borwein and Adrian
S.Lewis, Convex Analysis and
Nonlinear Optimization, Theory
andExamples, Springer 2000
Chapter2
Theory and Practice
Optimality Conditions
Jonathan M. Borwein and Adrian
S.Lewis, Convex Analysis and
Nonlinear Optimization, Theory
andExamples, Springer 2000
Cchapter2
Theory and Practice
Subgradients and convex functions.
Jonathan M. Borwein and Adrian
S.Lewis, Convex Analysis and
Nonlinear Optimization, Theory
and Examples, Springer 2000
Chapter3
Theory and Practice
5
Continuty of convex functions
Jonathan M. Borwein and Adrian
S.Lewis, Convex Analysis and
Nonlinear Optimization, Theory
and Examples, Springer 2000
Chapter4
Theory and Practice
6
Functional, increment of the functional
Naidu, D.S., Optimal Control
System, 2003 by CRC Press,
Chapter 2.1.1-2.1.2
Theory and Practice
7
Functional, increment of the functional,
Naidu, D.S., Optimal Control
System, 2003 by CRC Press,
Chapter 2.1.1-2.1.2
Theory and Practice
1
2
3
4
Preparation for Midterm Exam 50 min
8
9
10
Midterm 90 min
18.11.2015, 08.30-10.00
Differential and Variations, Optimum of
Function and Functional, The Basic Variational
Problem
Naidu, D.S., Optimal Control
System, 2003 by CRC Press,
Chapter 2.1.3 and Chapter 2.2
Naidu, D.S., Optimal Control
System, 2003 by CRC Pres
Chapter 2.1-2.2
Naidu, D.S., Optimal Control
The Basic Variational Problem, Euler-Lagrange
System, 2003 by CRC Press
Equations
Chapter 2.3
Theory and Practice
Theory and Practice
Theory and Practice
11
Extrema of Functions with Conditions,
Lagrange Multiplier Rules
Naidu, D.S., Optimal Control
System, 2003 by CRC Press
Chapter 2.5
Theory and Practice
12
Extrema of Functional with Conditions,
Naidu, D.S., Optimal Control
System, 2003 by CRC Press
Chapter 2.6
Theory and Practice
13
Variational Approach to Optimal Control
Systems
Naidu, D.S., Optimal Control
System, 2003 by CRC Press,
Chapter 2.7
Theory and Practice
14
Pontryagin Principle
Naidu, D.S., Optimal Control
System, 2003 by CRC Press
Chapter 2.7
Theory and Practice
15
Final exam
1) Jonathan M. Borwein and Adrian
Required Course Material (s) /Reading(s)/Text Book (s)
S.Lewis, Convex Analysis and
Nonlinear Optimization, Theory and Examples, Springer
2000
2) Donald E. Kirk, Optimal Control Theory,
Optimal control theory. 1970 or 1998
Recommended Course Material (s)/Reading(s)/Other
ASSESSMENT
Semester Activities/ Studies
NUMBER
WEIGHT in %
Mid- Term
1
40
Attendance
14
3
Quiz
4
5
Assignment (s)
2
2
Project
-
-
Laboratory
-
-
Field Studies (Technical Visits)
-
-
Presentation/ Seminar
-
-
Practice (Laboratory, Virtual Court, Studio Studies etc.)
-
-
Other (Placement/Internship etc.)
-
-
TOTAL
100
Contribution of Semester Activities/Studies to the Final Grade
50
Contribution of Final Examination/Final Project/ Dissertation to the Final Grade
50
TOTAL
100
CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME OUTCOMES
No Programme Outcomes
Level of
Contribution (1lowest/ 5highest)
1
1
2
To compare the given fundamental notions
To illustrate the given concepts with examples
2
3
4
5
x
x
To conclude results by using basic definitions
3
4
5
6
7
8
x
To demonstrate mathematical proofs clearly and correctly
x
To solve problems by analyzing mathematical theories, notions and data
x
To transfer the knowledge and solution offers related in the field
x
To use abstract thinking competence
x
To compare the given fundamental notions
x
ECTS /STUDENT WORKLOAD
NUMBER
UNIT
HOUR
TOTAL
(WORKLOAD)
Course Teaching Hour (14 weeks* total course hours)
14
Week
4
56
Preliminary Preparation and finalizing of course notes,
further self- study
14
2
28
Assignment (s)
3
3
9
ACTIVITIES
Presentation/ Seminars
Week
Number
Number
Quiz and Preparation for the Quiz
4
Number
2
8
Mid- Term(s)
1
Number
12
12
20
20
Project (s)
Number
Field Studies (Technical Visits, Investigate Visit etc.)
Number
Practice (Laboratory, Virtual Court, Studio Studies etc.)
Number
Final Examination/ Final Project/ Dissertation and
Preparation
Other (Placement/Internship etc.)
1
Number
Number
Total Workload
133
Total Workload/ 25
5.2
ECTS
5
ETHICAL RULES WITH REGARD TO THE COURSE (IF AVAILABLE)
ASSESSMENT and EVALUATION METHODS:
Final Grades will be determined according to the Yaşar University Associate Degree, Bachelor Degree and Graduate
Degree Education and Examination Regulation
PREPARED BY
Assoc. Prof. Shahlar Meherrem
UPDATED
12.09.2011
APPROVED