Linear Optimization Course

Course Description

Embark on an exciting journey into the world of linear optimization with this comprehensive introductory course offered by EPFLx. This course, designed for beginners, delves into the fascinating realm of mathematical problem-solving, focusing on linear optimization, duality, and the simplex algorithm. You'll gain a solid foundation in these essential concepts, which are crucial in various fields such as economics, engineering, and computer science.

What You'll Learn

• Formulation of optimization problems
• Representation and analysis of constraints in linear optimization
• Understanding and deriving dual problems
• Mastery of optimality conditions
• Implementation of the simplex algorithm
• Application of linear optimization concepts to real-world scenarios

Prerequisites

While no prior knowledge of optimization is required, students should have a strong background in linear algebra, including:

• Matrix operations
• Understanding of rank
• Familiarity with pivoting techniques

Although not mandatory, knowledge of Python programming language is beneficial for a deeper understanding of the algorithms presented in the course.

Course Content

• Introduction to linear optimization concepts
• Problem formulation and transformation techniques
• Geometric and algebraic representation of constraints
• Duality theory and its applications
• Sufficient and necessary conditions for optimal solutions
• The simplex method and its implementation
• Real-world applications of linear optimization

Who This Course Is For

• Mathematics and engineering students looking to expand their problem-solving skills
• Professionals in fields such as operations research, finance, and logistics
• Computer science students interested in algorithm design and optimization
• Anyone curious about mathematical modeling and its practical applications

Real-World Applications

• Supply chain management: Optimizing distribution networks and inventory levels
• Financial portfolio optimization: Maximizing returns while minimizing risks
• Transportation and logistics: Planning efficient routes and schedules
• Resource allocation: Optimizing the use of limited resources in manufacturing or project management
• Machine learning: Improving algorithm performance and efficiency
• Energy systems: Optimizing power distribution and renewable energy integration
• Telecommunications: Network design and capacity planning

Syllabus

1. Formulation
   • Simple examples of optimization problems
   • Transformation techniques
   • Problem characterization
2. Constraints
   • Geometric representation of constraints
   • Algebraic representation of constraints
3. Duality
   • Introduction to duality theory
   • Deriving dual problems
4. Optimality Conditions
   • Sufficient conditions for optimal solutions
   • Necessary conditions for optimal solutions
5. Simplex Method
   • Introduction to the simplex algorithm
   • Step-by-step implementation
   • Practical applications

By mastering linear optimization techniques, learners will be equipped with powerful tools to tackle complex decision-making problems and drive efficiency in their respective fields.

Enroll now and unlock the power of linear optimization!