EE443 NUMERICAL METHODS AND INTRODUCTION TO OPTIMIZATION
| Course Code: | 5670443 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 5.0 |
| Department: | Electrical and Electronics Engineering |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Assoc.Prof.Dr. LALE ALATAN |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will be able to
- describe finite precision arithmetic and identify numerical errors
- solve nonlinear equations numerically
- construct an interpolating polynomial that fits to given data points
- compute derivatives and integrals numerically
- formulate an optimization problem
- identify local and global optimality and convex problems
- solve unconstrained optimization problems with a single variable
- apply steepest descent, Newton’s and conjugate direction methods to solve multivariable unconstrained optimization problems
- solve linear system of equations in least squares sense
- apply Lagrange multiplier method and penalty function method to solve constrained optimization problems
Course Content
Finite precision arithmetic and numerical errors. Solution of linear system of equations. Numerical solution of nonlinear equations, interpolation, numerical differentiation and integration. Basic concepts of optimization, local and global optimality, convexity. Optimality conditions for unconstrained optimization; method of steepest descent, Newton s method, conjugate direction methods; least-squares solutions. Optimality conditions for problems with equality and inequality constraints; method of Lagrange multipliers and penalty function method.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
- explain how numbers are represented in computers
- classify numerical errors such as storage and truncation errors
- discuss the effects of arithmetic operations on the propagation of numerical errors
- give examples of numerical methods used to solve nonlinear equations
- construct a polynomial that fits the given data points
- use the build-in functions "polyfit, polyval" and "spline" in MATLAB
- give examples of numerical integration rules
- use the build-in functions "trapz, quad" and "dblquad" in MATLAB
- formulate a design problem as an optimization problem by identifying the objective function and constraints
- give examples of optimization algorithms developed for unconstrained optimization problems
- discuss the methods developed for constrained optimizaion problems.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics | ✔ | |||
| 2 | An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors | ✔ | |||
| 3 | An ability to communicate effectively with a range of audiences | ✔ | |||
| 4 | An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts. | ✔ | |||
| 5 | An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives | ✔ | |||
| 6 | An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions | ✔ | |||
| 7 | An ability to acquire and apply new knowledge as needed, using appropriate learning strategies | ✔ | |||