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Michel Bierlaire
Introduction to linear optimization, duality and the simplex algorithm.
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What's inside
Learning objectives
- Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem.
- Constraints: you will learn how to represent the constraints of a linear optimization problem, both from a geometric and algebraic point of views.
- Duality: you will learn how to derive a companion problem called the "dual".
- Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution.
- Simplex method: you will learn an algorithm to solve a linear optimization problem.
- The course is structured into 5 sections.
- Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem.
- Constraints: you will learn how to represent the constraints of a linear optimization problem, both from a geometric and algebraic point of views.
- Duality: you will learn how to derive a companion problem called the "dual".
- Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution.
- Simplex method: you will learn an algorithm to solve a linear optimization problem.
- The course is structured into 5 sections.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Helps learners with background in math and modeling derive a companion problem called the 'dual'
Suitable for learners with some background knowledge in formulating, transforming and characterizing optimization problems
May need additional materials for learners who have not taken some courses in linear algebra and optimization
Provides a geometric and algebraic point of view
Taught by Michel Bierlaire, who is recognized for their work in transportation and logistics
Adequate materials including videos, readings and discussions
Save this course
Save Optimization: principles and algorithms - Linear optimization to your list so you can find it easily later:
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Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Optimization: principles and algorithms - Linear optimization with these
activities:
Organize Your Notes and Course Materials
Show steps
Create a comprehensive resource that will help you stay organized and retain information.
Show steps
-
Compile your notes, handouts, assignments, and quizzes in a single location.
-
Review and organize the materials regularly to reinforce your understanding.
-
Identify any gaps in your understanding and seek additional resources to fill them.
Read Introduction to Linear Optimization
Show steps
Prepare yourself with a foundational understanding of linear optimization.
View
Introduction to Linear Optimization (Athena...
on Amazon
Show steps
-
Read the introduction and first chapter to familiarize yourself with the basic concepts.
-
Work through the examples and exercises to reinforce your understanding.
-
Attend office hours or ask questions online to clarify any concepts you don't understand.
Explore Online Tutorials on Linear Optimization
Show steps
Supplement your learning with additional resources to reinforce your understanding.
Show steps
-
Search for reputable online tutorials or courses on linear optimization.
-
Review the material provided and complete any practice exercises.
-
Use the tutorials to clarify any areas where you need extra support.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Join a Study Group for Linear Optimization
Show steps
Collaborate with other students to enhance your understanding and problem-solving skills.
Show steps
-
Find a study group or create your own with classmates.
-
Set regular meeting times and establish clear goals.
-
Review course material, work on practice problems, and discuss complex concepts together.
Solve Linear Optimization Practice Problems
Show steps
Build your problem-solving skills by practicing with a variety of linear optimization problems.
Show steps
-
Find a set of practice problems online or in a textbook.
-
Set aside regular time to work on the problems.
-
Check your solutions against the provided answer key or ask for help if needed.
Create a Linear Optimization Model for a Real-World Problem
Show steps
Deepen your understanding of linear optimization by applying it to a real-world problem.
Show steps
-
Identify a real-world problem that can be modeled as a linear optimization problem.
-
Formulate the problem as a linear optimization model.
-
Use a solver to solve the model and analyze the results.
Become a Peer Tutor for Linear Optimization
Show steps
Strengthen your understanding by helping others master linear optimization concepts.
Show steps
-
Apply to become a peer tutor through your university or online platforms.
-
Prepare materials and resources to support your tutoring sessions.
-
Meet with students regularly to provide guidance and assistance.
Develop a Linear Optimization App
Show steps
Integrate your linear optimization knowledge into a practical project.
Show steps
-
Identify a problem or area where a linear optimization app would be beneficial.
-
Design and develop the app, using appropriate programming tools and algorithms.
-
Test the app thoroughly and make necessary revisions.
Organize Your Notes and Course Materials
Show steps
Create a comprehensive resource that will help you stay organized and retain information.
Show steps
Show steps
Show steps
- Compile your notes, handouts, assignments, and quizzes in a single location.
- Review and organize the materials regularly to reinforce your understanding.
- Identify any gaps in your understanding and seek additional resources to fill them.
Read Introduction to Linear Optimization
Show steps
Prepare yourself with a foundational understanding of linear optimization.
View
Introduction to Linear Optimization (Athena...
on Amazon
Show steps
Show steps
Show steps
- Read the introduction and first chapter to familiarize yourself with the basic concepts.
- Work through the examples and exercises to reinforce your understanding.
- Attend office hours or ask questions online to clarify any concepts you don't understand.
Explore Online Tutorials on Linear Optimization
Show steps
Supplement your learning with additional resources to reinforce your understanding.
Show steps
Show steps
Show steps
- Search for reputable online tutorials or courses on linear optimization.
- Review the material provided and complete any practice exercises.
- Use the tutorials to clarify any areas where you need extra support.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Join a Study Group for Linear Optimization
Show steps
Collaborate with other students to enhance your understanding and problem-solving skills.
Show steps
Show steps
Show steps
- Find a study group or create your own with classmates.
- Set regular meeting times and establish clear goals.
- Review course material, work on practice problems, and discuss complex concepts together.
Solve Linear Optimization Practice Problems
Show steps
Build your problem-solving skills by practicing with a variety of linear optimization problems.
Show steps
Show steps
Show steps
- Find a set of practice problems online or in a textbook.
- Set aside regular time to work on the problems.
- Check your solutions against the provided answer key or ask for help if needed.
Create a Linear Optimization Model for a Real-World Problem
Show steps
Deepen your understanding of linear optimization by applying it to a real-world problem.
Show steps
Show steps
Show steps
- Identify a real-world problem that can be modeled as a linear optimization problem.
- Formulate the problem as a linear optimization model.
- Use a solver to solve the model and analyze the results.
Become a Peer Tutor for Linear Optimization
Show steps
Strengthen your understanding by helping others master linear optimization concepts.
Show steps
Show steps
Show steps
- Apply to become a peer tutor through your university or online platforms.
- Prepare materials and resources to support your tutoring sessions.
- Meet with students regularly to provide guidance and assistance.
Develop a Linear Optimization App
Show steps
Integrate your linear optimization knowledge into a practical project.
Show steps
Show steps
Show steps
- Identify a problem or area where a linear optimization app would be beneficial.
- Design and develop the app, using appropriate programming tools and algorithms.
- Test the app thoroughly and make necessary revisions.
Career center
Learners who complete Optimization: principles and algorithms - Linear optimization will develop knowledge and skills
that may be useful to these careers:
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts solve complex problems by applying advanced analytical methods to gather and analyze data. They use their findings to improve efficiency and productivity. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Management Consultant
Management Consultant
Management Consultants help organizations improve their performance. They use their analytical skills to identify problems and develop solutions. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Data Scientist
Data Scientist
Data Scientists use their skills in mathematics, statistics, and computer science to extract knowledge from data. They use this knowledge to solve problems and make predictions. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Financial Analyst
Financial Analyst
Financial Analysts use their knowledge of finance and economics to make investment recommendations. They also help companies make decisions about how to allocate their resources. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Actuary
Actuary
Actuaries use their knowledge of mathematics and statistics to assess risk. They use this knowledge to help companies make decisions about how to manage their risks. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. They use their knowledge of computer science to solve problems and create solutions. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Operations Manager
Operations Manager
Operations Managers oversee the day-to-day operations of a company. They are responsible for ensuring that the company's operations are efficient and effective. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Business Analyst
Business Analyst
Business Analysts use their knowledge of business and technology to help companies improve their performance. They use their analytical skills to identify problems and develop solutions. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Systems Analyst
Systems Analyst
Systems Analysts design, develop, and maintain computer systems. They use their knowledge of computer science and systems engineering to solve problems and create solutions. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Statistician
Statistician
Statisticians use their knowledge of statistics to collect, analyze, and interpret data. They use this knowledge to solve problems and make predictions. This course can help you develop the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. You will learn how to represent constraints, derive dual problems, and use the simplex method to find optimal solutions.
Economist
Economist
Economists use their knowledge of economics to analyze and interpret economic data. They use this knowledge to make predictions about the economy and to develop policies to improve economic performance. This course may help you develop some of the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. However, you should be aware that a Master's or Ph.D. degree is typically required to enter this field.
Market Researcher
Market Researcher
Market Researchers use their knowledge of marketing and research methods to collect and analyze data about consumer behavior. They use this knowledge to help businesses develop and market their products and services. This course may help you develop some of the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. However, you should be aware that a Master's degree is often required for this role.
Financial Planner
Financial Planner
Financial Planners help individuals and families plan for their financial future. They use their knowledge of finance and investment to develop financial plans that meet their clients' needs. This course may help you develop some of the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. However, you should be aware that a Master's degree and relevant certifications are typically required for this role.
Teacher
Teacher
Teachers teach students at all levels, from elementary school to college. They use their knowledge of their subject matter to develop and deliver lesson plans that meet the needs of their students. This course may help you develop some of the skills you need to succeed in this role by teaching you how to formulate and solve optimization problems. However, you should be aware that a teaching certification is typically required for this role.
Lawyer
Lawyer
Lawyers represent clients in legal matters. They use their knowledge of the law to advise clients on their rights and responsibilities, and to represent them in court. This course may help you develop some of the analytical skills you need to succeed in this role. However, you should be aware that a law degree is required for this role.
For more career information including salaries, visit:
OpenCourser.com/course/l9g32z/optimization
Reading list
We've selected ten books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Optimization: principles and algorithms - Linear optimization.
Provides a comprehensive introduction to linear optimization, covering topics such as formulating linear optimization problems, solving them using the simplex method, and understanding duality theory. It valuable resource for students and practitioners who want to learn more about linear optimization.
Provides a comprehensive introduction to convex optimization, covering topics such as convex sets, convex functions, and optimization algorithms. It valuable resource for students and practitioners who want to learn more about convex optimization.
Provides a comprehensive introduction to nonlinear programming, covering topics such as unconstrained optimization, constrained optimization, and global optimization. It valuable resource for students and practitioners who want to learn more about nonlinear programming.
Provides a comprehensive introduction to combinatorial optimization, covering topics such as graph theory, network flows, and matroids. It valuable resource for students and practitioners who want to learn more about combinatorial optimization.
Provides a comprehensive introduction to reinforcement learning, covering topics such as Markov decision processes, value functions, and reinforcement learning algorithms. It valuable resource for students and practitioners who want to learn more about reinforcement learning.
Save
Provides a comprehensive introduction to machine learning, covering topics such as supervised learning, unsupervised learning, and reinforcement learning. It valuable resource for students and practitioners who want to learn more about machine learning.
Save
Provides a comprehensive introduction to deep learning, covering topics such as neural networks, convolutional neural networks, and recurrent neural networks. It valuable resource for students and practitioners who want to learn more about deep learning.
Save
Provides a comprehensive introduction to computer vision, covering topics such as image processing, feature detection, and object recognition. It valuable resource for students and practitioners who want to learn more about computer vision.
Provides a comprehensive introduction to natural language processing, covering topics such as part-of-speech tagging, parsing, and machine translation. It valuable resource for students and practitioners who want to learn more about natural language processing.
Provides a comprehensive introduction to artificial intelligence, covering topics such as search, planning, and machine learning. It valuable resource for students and practitioners who want to learn more about artificial intelligence.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/l9g32z/optimization
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Effort
6 to 8 hours per week for 5 weeks
Level
Introductory
Via
edX
Institution
École Polytechnique Fédérale de Lausanne
Instructor
Michel Bierlaire
Language
English
Transcript
English
Good to know
Helps learners with background in math and modeling derive a companion problem called the 'dual'
Suitable for learners with some background knowledge in formulating, transforming and characterizing optimization problems
May need additional materials for learners who have not taken some courses in linear algebra and optimization
Provides a geometric and algebraic point of view
Taught by Michel Bierlaire, who is recognized for their work in transportation and logistics
Adequate materials including videos, readings and discussions
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