- Understanding the Concept of Optimization: Students will learn the basic principles of optimization, including defining objectives, constraints, decision variables, and how to model real-world problems into mathematical optimization frameworks.
- Solving Unconstrained Optimization Problems: Students will explore unconstrained optimization problems, learning popular algorithms like the gradient descent method, Newton’s method, and the steepest descent method.
- Solving Constrained Optimization Problems: The course will delve into constrained optimization problems, focusing on techniques such as the Lagrange multiplier method, linear programming, and quadratic programming.
- Linear Optimization: Students will grasp the concept of linear optimization and become familiar with the Simplex method for solving linear programming problems.
- Non-Linear Optimization: This section will introduce students to non-linear optimization problems and cover algorithms like the Nelder-Mead method and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.
- Integer Optimization: Students will explore optimization problems with discrete decision variables, such as the branch and bound method and the branch and cut method.
- Applications in Various Fields: The course will showcase real-world applications of optimization in fields like engineering, economics, logistics, finance, and data science.
- Optimization Software: Students will gain hands-on experience with optimization software packages like MATLAB, Python libraries (e.g., SciPy, CVXPY), or dedicated optimization tools.
Course Format: The course will be delivered through a combination of lectures, interactive discussions, problem-solving sessions, and practical exercises using optimization software. Students will have the opportunity to work on individual and group projects, applying optimization techniques to solve real-world problems.
Prerequisites: This course assumes a solid foundation in mathematics, including calculus, linear algebra, and basic programming skills. Students with prior exposure to mathematical modeling or operations research will find the content particularly relevant, but the course is open to all enthusiastic learners willing to explore the world of optimization.
Join us on this exciting journey into the realm of optimization and equip yourself with powerful problem-solving tools applicable across various domains. Whether you are a budding engineer, economist, or data scientist, understanding optimization will undoubtedly enrich your problem-solving skills and open new avenues for research and innovation. Let’s optimize our knowledge together!