| 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) |
Having advanced theoretical and practical knowledge supported by textbooks, application tools and other resources containing current information in the field. |
3 |
| 2) |
Ability to use advanced theoretical and practical knowledge acquired in the field. |
3 |
| 3) |
Ability to interpret and evaluate data, identify and analyze problems, and develop solution suggestions based on research and evidence, using the advanced knowledge and skills acquired in the field. |
3 |
| 4) |
To be able to inform relevant people and institutions on issues related to the field; Ability to convey thoughts and solution suggestions to problems in written and oral form. |
3 |
| 5) |
Ability to share one's thoughts on issues related to one's field and solutions to problems, supported by quantitative and qualitative data, with experts and non-experts. |
3 |
| 6) |
Ability to organize and implement projects and events for the social environment in which one lives with awareness of social responsibility. |
|
| 7) |
Ability to monitor knowledge in the field and communicate with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level. |
|
| 8) |
Ability to use information and communication technologies along with computer software at least at the Advanced Level of the European Computer Usage License required by the field. |
|
| 9) |
Acting in accordance with social, scientific, cultural and ethical values during the collection, interpretation, application and announcement of the results of data related to the field. |
|
| 10) |
Having sufficient awareness about the universality of social rights, social justice, quality culture and protection of cultural values, environmental protection, occupational health and safety. |
|
| 11) |
Ability to evaluate the advanced knowledge and skills acquired in the field with a critical approach. |
3 |
| 12) |
Ability to identify learning needs and direct learning |
|
| 13) |
Being able to develop a positive attitude towards lifelong learning. |
|
| 14) |
Ability to independently carry out an advanced study related to the field. |
|
| 15) |
Ability to take responsibility individually and as a team member to solve unforeseen complex problems encountered in field-related applications. |
|
| 16) |
Ability to plan and manage activities aimed at the development of the employees under his/her responsibility within the framework of a project. |
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Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE