Introduction to Nonlinear Programming

Course Code:

ISE 425

Course Type:

Area Elective

Credits:

3

Theoric:

3

Practice:

0

Laboratory Hour:

0

ECTS:

5

Prerequisite Courses:

Computational Methods for Industrial Engineers

Calculus II

Course Language:

English

Course Objectives:

The aim of this course is to study the theory of nonlinear optimization and solutions methods for nonlinear optimization problems, which have many applications in the field of industrial engineering.

Course Content:

Single variable optimization, multi-variable unconstrained optimization, equality constrained optimization (Lagrangian method) and inequality constrained optimization (KKT conditions). Convex, concave functions,

convex sets and convex optimization problems. Iterative solution methods.

Course Methodology:

1: Lecture by instructor, 2: Lecture by instructor with class discussion, 3: Problem solving by instructor, 5: Problem solving assignment.

Course Evaluation Methods:

A: Written exam, C: quiz, E: Homework.

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Course Learning Outcomes

Course Learning Outcomes	Detailed Program Outcomes	Teaching Methods	Assessment Methods
Knows concepts of local and global optimal solution.	1a, 6c	1,2,3,5	A,C,E
Knows optimality conditions for functions of single and multiple variables. Solves unconstrained optimization problems using optimality conditions.	1a, 6c	1,2,3,5	A,C,E
Solves equality constrained optimization problems using Lagrangian approach.	1a, 6c	1,2,3,5	A,C,E
Solves inequality constrained optimization problems using KKT conditions for optimality.	1a, 6c	1,2,3,5	A,C,E
Solves optimization problems of single and multiple variables using iterative numerical algorithms. Write computer programs for this purpose.	1a, 4a, 4b, 6c	1,2,3,5	A,C,E
Knows convex/concave functions and convex sets. Uses mathematical conditions for convexity to identify convex optimization problems.	1a, 6c	1,2,3,5	A,C,E

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1-2	Introduction to nonlinear programming	Textbook, Lecture notes, Computer, MATLAB/OCTAVE
3-5	Single variable unconstrained optimization problems, solution methods and programming applications	Textbook, Lecture notes, Computer, MATLAB/OCTAVE
6-9	Multi-variable unconstrained optimization problems, solution methods and programming applications	Textbook, Lecture notes, Computer, MATLAB/OCTAVE
10-11	Equality constrained optimization problems, solution methods and programming applications	Textbook, Lecture notes, Computer, MATLAB/OCTAVE
12-14	Inequality constrained optimization problems, solution methods and programming applications	Textbook, Lecture notes, Computer, MATLAB/OCTAVE

Recommended Sources

RECOMMENDED SOURCES
Textbooks	CB1: Winston, W.L. “Operations Research Applications and Algorithms”, Fourth Edition, Cengage Learning, 2003 CB2: Nocedal, J.; Wright, S, “Numerical Optimization”, Second Edition, Springer, 2006 CB3: Bertsekas, D. P. “Nonlinear Programming”, Second Edition, Athena Scientific,1999
Additional Resources	Lecture Notes

Material Sharing

MATERIAL SHARING
Documents	Lecture notes
Assignments	Homework assignments
Quizzes	Quiz questions
Exams	Exam questions

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-term	2	83
Quiz/Homework	5	17
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM OUTCOMES
No	Program Learning Outcomes	check √
1a	Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline,	√
1b	Ability to use theoretical and applied knowledge in these areas in complex engineering problems.
2a	Ability to identify, formulate, and solve complex engineering problems,
2b	Ability to select and apply proper analysis and modeling methods for this purpose.
3a	Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result,
3b	Ability to apply modern design methods for this purpose.
4a	Ability to devise, select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice.	√
4b	Ability to employ information technologies effectively.	√
5a	Ability to design experiments for investigating complex engineering problems or discipline specific research questions,
5b	Ability to conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6a	Ability to work efficiently in intra-disciplinary teams,
6b	Ability to work efficiently in multi-disciplinary teams,
6c	Ability to work individually.	√
7a	Ability to communicate effectively in Turkish, both orally and in writing,
7b	Knowledge of a minimum of one foreign language,
7c	Ability to write effective reports and comprehend written reports, prepare design and production reports,
7d	Ability to make effective presentations,
7e	Ability to give and receive clear and intelligible instructions.
8a	Recognition of the need for lifelong learning, ability to access information, ability to follow developments in science and technology,
8b	Ability to continue to educate him/herself.
9a	Consciousness to behave according to ethical principles and professional and ethical responsibility.
9b	Knowledge on standards used in engineering practice.
10a	Knowledge about business life practices such as project management, risk management, change management.
10b	Awareness in entrepreneurship and innovation.
10c	Knowledge about sustainable development.
11a	Knowledge about the global and social effects of engineering practices on health, environment, and safety,
11b	Knowledge about contemporary issues of the century reflected into the field of engineering.
11c	Awareness of the legal consequences of engineering solutions.

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (Excluding the exam hours: 12x Total course hours)	12	3	36
Hours for study and/or exam (Quizzes/Homework)	5	5	25
Hours for off-the-classroom study (Midterms)	2	15	30
Hours for off-the-classroom study (Final)	1	20	20
Midterm exam	2	2	4
Final exam	1	2	2
Total Work Load			117
Total Work Load / 25 (h)			4,68
ECTS Credit of the Course			5

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Introduction to Nonlinear Programming

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