| Course Objectives: |
To understand basic linear and non-linear optimization methods,
Being able to formulate optimization problems correctly
To be able to apply optimization methods to engineering problems
Being able to solve a complex problem |
| Course Content: |
Definition and classification of optimization problem, Lagrange Formulation, Karush-Kuhn Tucker conditions, Classical Optimization Techniques, Single-variable Multi-variable Constrained-Unconstrained Optimization, Linear Programming, Simplex Algorithm, Duality, Non-Linear Programming, One-Dimensional Minimization, Elimination Methods ( Unlimited Search, Golden Section Search, Steepest Descent Method), Interpolation Methods (Quadratic and Cubic Interpolation Methods, Newton Method, Semi-Newton Method), Unlimited Optimization Techniques, Direct Access and Indirect Access (Descent) Methods |
| Week |
Subject |
Related Preparation |
| 1) |
Introduction to Optimization: Definition of the optimization problem, classification of optimization problems, basic information about optimization techniques |
Course Notes |
| 2) |
Mathematical Background (Maximums and minimums of functions, convex and concave functions) |
Course Notes |
| 3) |
Classical Optimization Techniques-1: Univariate Optimization, Multivariate Unconstrained Optimization |
Course Notes |
| 4) |
Classical Optimization Techniques-2: Multivariate Equality Constrained Optimization, Direct Substitution, Constrained Variation and Lagrange Multipliers Methods |
Course Notes |
| 5) |
Classical Optimization Techniques-3: Optimization with Multivariate Inequality Constraints, Kuhn-Tucker Conditions, Characterization of Constraint, Convex Programming Problem |
Course Notes |
| 6) |
Linear Programming 1: Linear Programming Applications, Standard Form of Linear Programming Problem, Pivoting |
Course Notes |
| 7) |
Linear Programming 2: Simplex Algorithm |
Course Notes |
| 8) |
Midterm Exam |
|
| 9) |
Determining the Optimal Point, Possible Solution, Improving the Non-Optimal Basic Possible Solution, Two Phases of the Simplex Method |
Course Notes |
| 10) |
Nonlinear Programming 1: One-Dimensional Minimization Methods, Elimination Methods (Fibonacci, Golden Section, Bisection), Comparison of Methods |
Course Notes |
| 11) |
Nonlinear Programming 2: Interpolation Methods (Quadratic and cubic interpolation), Direct Methods (Newton, Semi-Newton, Secant Methods) |
Course Notes |
| 12) |
Nonlinear Programming 3: Unconstrained Optimization Techniques, Convergence Speed, Scaling of Design Variables |
Course Notes |
| 13) |
Direct Search Methods (Random jumping, Random walk, Grid Search, Univariate, Simplex methods) |
Course Notes |
| 14) |
Indirect Search Methods (Steepest Descent, Fletcher-Reeves Methods) |
Course Notes |
| 15) |
Presentations of final projects |
|
| 16) |
Final Exams |
|
| 17) |
Final Exams |
|
| |
Program Outcomes |
Level of Contribution |
| 1) |
Ability to utilize advanced theoretical and applied knowledge in the field. |
3 |
| 2) |
Using the advanced knowledge and skills acquired in the field, being able to interpret and evaluate data, identify problems, analyze them, and develop solution proposals based on research and evidence. |
3 |
| 3) |
Being able to organize and implement projects and activities for the social environment in which one lives with a sense of social responsibility. |
|
| 4) |
Being able to follow information in one foreign language at least at the European Language Portfolio B1 General Level and communicate with colleagues in the field. |
|
| 5) |
Ability to use information and communication technologies together with at least European Computer Driving License Advanced Level computer software, as required by the field. |
|
| 6) |
Being able to evaluate advanced knowledge and skills in the field critically. |
3 |
| 7) |
Identifying learning needs and being able to direct learning. |
3 |
| 8) |
Developing a positive attitude towards lifelong learning. |
|
| 9) |
Acting in accordance with social, scientific, cultural, and ethical values in the stages of collecting, interpreting, applying, and announcing the results related to the field. |
|
| 10) |
Having sufficient awareness about the universality of social rights, social justice, quality culture, preservation of cultural values, as well as environmental protection, occupational health, and safety. |
|
| 11) |
Being able to conduct an advanced study independently in the field. |
|
| 12) |
To take responsibility individually and as a team member to solve complex problems encountered in the field of application, which are unforeseen. |
|
| 13) |
Being able to plan and manage activities for the development of those under their responsibility within the framework of a project. |
3 |
| 14) |
Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources. |
3 |
| 15) |
Being able to inform relevant individuals and institutions about the field; expressing their thoughts and solution proposals for problems both in written and verbal form. |
3 |
| 16) |
Being able to share your thoughts and solutions regarding subjects related to the field with both experts and non-experts, supported by quantitative and qualitative data. |
3 |
Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE