MATH402 INTRODUCTION TO OPTIMIZATION
| Course Code: | 2360402 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Fall Semesters. |
Course Objectives
Computational science, engineering, and applied mathematics face a growing need to develop algorithms, methods, and simulation codes that solve difficult and large-scale problems. Solutions are sought that can provide designs, controls, and inversion results for the best selection of input parameters. Optimization algorithms can provide computer scientist, engineers, and mathematicians the ability to find the most suitable solution, automate execution, and achieve efficient convergence rates.
This course is designed for undergraduate students majoring in mathematics as well as mathematically inclined engineering students. At the end of this course, the student will:
- learn the central ideas behind algorithms for the numerical solution of differentiable optimization problems by presenting key methods for both unconstrained and constrained optimization, as well as providing theoretical justification as to why they succeed;
- learn the computational tools to solving optimization problems on computers once a mathematical formulation has been found.
Course Content
The importance of optimization, basic definition and facts on convex analysis. Theory of linear programming and convex prog-ramming, simplex method and its applications, nonlinear programming, search methods, basic ideas of classical variational calculus, optimal control theory. Pontraygin`s maximum principle and dynamic programming, linear theory of optimal control.
Course Learning Outcomes
Upon successful completion of this course, the student will be able to
- recognize the character of an optimization problem (constrained, unconstrained, smooth, nonsmooth) and choose appropriate algorithms for their solutions;
- understand the basic convergence analysis for the learned optimization methods;
- solve optimization problems using MATLAB, Phyton, or other commercial software;
- how to use and design efficient numerical optimization algorithms for their own research problems.