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Michel Bierlaire
Introduction to unconstrained nonlinear optimization, Newton’s algorithms and descent methods.
Register for this course and see more details by visiting:
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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.
- Objective function: you will review the mathematical properties of the objective function that are important in optimization.
- Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution.
- Solving equations, newton: this is a reminder about newton's method to solve nonlinear equations.
- Newton's local method: you will see how to interpret and adapt newton's method in the context of optimization.
- Descent methods: you will learn the family of descent methods, and its connection with newton's method.
- The course is structured into 6 sections:
- Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem.
- Objective function: you will review the mathematical properties of the objective function that are important in optimization.
- Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution.
- Solving equations, newton: this is a reminder about newton's method to solve nonlinear equations.
- Newton's local method: you will see how to interpret and adapt newton's method in the context of optimization.
- Descent methods: you will learn the family of descent methods, and its connection with newton's method.
- The course is structured into 6 sections:
Traffic lights
Traffic lights
Read about what's good
what should give you pause and
possible dealbreakers
Combines theory and practice, leading to a holistic understanding of optimization
Provides a strong foundation in the fundamentals of optimization
Employs clear and concise explanations, making the concepts accessible to learners
Covers a range of optimization methods, providing learners with a broad understanding
Requires a strong mathematical background, which may limit accessibility for some learners
May not be suitable for learners seeking a more practical approach to optimization
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Reviews summary
Core principles of unconstrained optimization
According to students, this course offers a strong theoretical foundation in unconstrained nonlinear optimization, covering Newton's methods and descent algorithms in depth. Many found the lectures to be clear and well-structured, providing a solid understanding of mathematical principles. However, some learners noted the course is highly rigorous and mathematically demanding, often requiring a strong prerequisite knowledge in linear algebra and calculus. A common point of feedback highlights a limited focus on practical applications or coding exercises, suggesting it's more suited for those seeking conceptual mastery rather than hands-on implementation. The course is considered excellent for a deep theoretical dive but might require supplemental resources for practical skills.
Course is fast-paced and challenging, requiring dedication and time.
"The pace is quite fast; I had to re-watch lectures multiple times to keep up with the new concepts."
"This course is definitely challenging, but rewarding if you put in the effort and dedicate enough time."
"I found the level of detail and rapid introduction of new topics quite demanding, but manageable."
Instructor's explanations are praised for clarity and effectiveness.
"The instructor's explanations were incredibly clear, simplifying what could have been very complex concepts."
"I found the lecture delivery engaging and easy to follow, which really helped in understanding the algorithms."
"The way the instructor breaks down each principle makes it digestible, even for challenging topics."
Provides a deep and clear understanding of core optimization principles.
"The course provides a very solid theoretical background on unconstrained nonlinear optimization, making complex topics understandable."
"I really appreciated how the lectures broke down Newton's algorithms and descent methods with such clarity, building a strong foundation."
"This course helped me develop a robust conceptual understanding of optimization principles that I can now apply to other areas."
Focuses heavily on theory with minimal hands-on coding or examples.
"I wished there were more coding examples or practical exercises to complement the dense theoretical content."
"While the theory is excellent, I felt a lack of real-world application or implementation details in Python/Matlab."
"This course is great for theory, but I had to seek external resources for actual coding practice."
Requires a strong mathematical background to fully grasp the material.
"I found it challenging without a very solid background in linear algebra and advanced calculus; the math is intense."
"I struggled with some of the derivations because my math skills weren't as sharp as needed for this level."
"Prospective students should be aware that strong mathematical rigor is expected; this isn't for the faint of heart."
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 - Unconstrained nonlinear optimization with these
activities:
Review prerequisite material: calculus, linear algebra
Show steps
Ensure you are comfortable with these mathematical foundations
Browse courses on
Linear Algebra
Show steps
-
Review lecture notes and textbooks
-
Practice solving problems
-
Seek help from a math tutor or online resources if needed
Attend a study group meeting with your classmates
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Collaborate with peers to discuss course concepts and solve problems
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-
Form or join a study group with classmates
-
Meet regularly to review lectures, work on assignments, and discuss problems
-
Take turns explaining concepts and leading discussions
Complete practice exercises on Newton's method
Show steps
Develop fluency in applying Newton's method to solve optimization problems
Browse courses on
Newton's Method
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-
Find practice problems online or in a textbook
-
Solve the problems using Newton's method
-
Check your answers against provided solutions
Three other activities
Expand to see all activities and additional details
Show all six activities
Solve optimization problems in different domains
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Gain experience applying optimization techniques to real-world problems
Browse courses on
Optimization
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-
Find optimization problems related to fields like finance, engineering, or data science
-
Formulate the problem mathematically
-
Solve the problem using optimization methods learned in the course
Attend a workshop on practical optimization techniques
Show steps
Gain practical insights and hands-on experience in optimization
Browse courses on
Optimization Techniques
Show steps
-
Find a workshop on practical optimization techniques
-
Register for the workshop and attend the sessions
-
Actively participate in discussions and exercises
Develop a visual representation of gradient descent
Show steps
Enhance your understanding and visualize the concept
Browse courses on
Gradient Descent
Show steps
-
Identify a visualization tool, e.g., Python's Matplotlib or GeoGebra
-
Plot the gradient descent algorithm for a given function and initial point
-
Use color or animation to highlight the path taken by the algorithm
Review prerequisite material: calculus, linear algebra
Show steps
Ensure you are comfortable with these mathematical foundations
Browse courses on
Linear Algebra
Show steps
Show steps
Show steps
- Review lecture notes and textbooks
- Practice solving problems
- Seek help from a math tutor or online resources if needed
Attend a study group meeting with your classmates
Show steps
Collaborate with peers to discuss course concepts and solve problems
Show steps
Show steps
Show steps
- Form or join a study group with classmates
- Meet regularly to review lectures, work on assignments, and discuss problems
- Take turns explaining concepts and leading discussions
Complete practice exercises on Newton's method
Show steps
Develop fluency in applying Newton's method to solve optimization problems
Browse courses on
Newton's Method
Show steps
Show steps
Show steps
- Find practice problems online or in a textbook
- Solve the problems using Newton's method
- Check your answers against provided solutions
Three other activities
Expand to see all activities and additional details
Show all six activities
Solve optimization problems in different domains
Show steps
Gain experience applying optimization techniques to real-world problems
Browse courses on
Optimization
Show steps
Show steps
Show steps
- Find optimization problems related to fields like finance, engineering, or data science
- Formulate the problem mathematically
- Solve the problem using optimization methods learned in the course
Attend a workshop on practical optimization techniques
Show steps
Gain practical insights and hands-on experience in optimization
Browse courses on
Optimization Techniques
Show steps
Show steps
Show steps
- Find a workshop on practical optimization techniques
- Register for the workshop and attend the sessions
- Actively participate in discussions and exercises
Develop a visual representation of gradient descent
Show steps
Enhance your understanding and visualize the concept
Browse courses on
Gradient Descent
Show steps
Show steps
Show steps
- Identify a visualization tool, e.g., Python's Matplotlib or GeoGebra
- Plot the gradient descent algorithm for a given function and initial point
- Use color or animation to highlight the path taken by the algorithm
Career center
Learners who complete Optimization: principles and algorithms - Unconstrained nonlinear optimization will develop knowledge and skills
that may be useful to these careers:
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical modeling to analyze financial data and make investment recommendations. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating financial models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Data Scientist
Data Scientist
Data Scientists use machine learning and other statistical methods to analyze data and extract insights. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating machine learning models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers design and build machine learning models. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating machine learning models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical methods to improve the efficiency and effectiveness of business operations. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating operations research models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Financial Analyst
Financial Analyst
Financial Analysts use financial data to make investment recommendations. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating financial models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Actuary
Actuary
Actuaries use mathematical and statistical methods to assess risk and uncertainty. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating actuarial models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Statistician
Statistician
Statisticians use statistical methods to analyze data and draw conclusions. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating statistical models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Economist
Economist
Economists use economic theory and data to analyze economic issues. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating economic models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Mathematician
Mathematician
Mathematicians develop and apply mathematical theories and techniques to solve problems in a wide range of fields. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating mathematical models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Computer Scientist
Computer Scientist
Computer Scientists design and develop computer systems and applications. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating computer algorithms. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating software algorithms. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Data Analyst
Data Analyst
Data Analysts use data to identify trends and patterns. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating data analysis algorithms. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Business Analyst
Business Analyst
Business Analysts use data and analysis to improve business processes. This course can help you develop the skills needed to succeed in this role by providing a strong foundation in optimization techniques, which are essential for developing and evaluating business analysis models. You will learn how to formulate and solve optimization problems, as well as how to use descent methods and Newton's method to find optimal solutions.
Project Manager
Project Manager
Project Managers plan and execute projects to achieve specific goals.
For more career information including salaries, visit:
OpenCourser.com/course/jqcnpv/optimization
Reading list
We've selected 13 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 - Unconstrained nonlinear optimization.
Save
Comprehensive treatment of nonlinear optimization, a branch of optimization that deals with problems where the objective function or constraints are nonlinear. It is written by leading experts in the field, and it is known for its clarity and rigor.
Comprehensive and up-to-date treatment of optimization, a branch of mathematics that deals with finding the best possible solution to a given problem. It is written by leading experts in the field, and it is known for its clarity and rigor.
Comprehensive treatment of nonlinear optimization, a branch of optimization that deals with problems where the objective function or constraints are nonlinear. It is written by a leading expert in the field, and it is known for its clarity and rigor.
Comprehensive and up-to-date treatment of convex optimization, a powerful technique for solving a wide range of optimization problems. It is written by a leading expert in the field, and it is known for its clarity and rigor.
Classic textbook on nonlinear programming, a branch of optimization that deals with problems where the objective function or constraints are nonlinear. It comprehensive and well-written book that is suitable for both students and practitioners.
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Provides an accessible introduction to optimization, with a focus on data analysis. It covers both theoretical concepts and practical algorithms, and it is written in a clear and engaging style.
Concise and well-written introduction to optimization, a branch of mathematics that deals with finding the best possible solution to a given problem. It is suitable for both students and practitioners.
Provides a comprehensive treatment of optimization theory and algorithms.
Is an introduction to stochastic optimization, a branch of optimization that deals with problems where the objective function or constraints are random. It is written by a leading expert in the field, and it is known for its clarity and rigor.
Comprehensive reference for numerical optimization.
Provides a comprehensive treatment of nonlinear programming.
Provides a thorough treatment of convex optimization.
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Provides a practical introduction to optimization for data science.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/jqcnpv/optimization
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Effort
6 to 8 hours per week for 6 weeks
Level
Introductory
Via
edX
Institution
École Polytechnique Fédérale de Lausanne
Instructor
Michel Bierlaire
Language
English
Transcript
English
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