Convex optimization is a powerful technique for interpreting information effectively, helping people and industries around the world solve large-scale problems. Knowing how to apply convex optimization is a highly-valued skill and a rewarding achievement for anyone.
If you’re planning to learn convex optimization, you’ve come to the right place. Use this guide to clear all your doubts regarding what the learning process entails. From understanding what it is all about, to finding the best online convex optimization courses and resources, we’ve got you covered.
What Is Convex Optimization?
Convex optimization is a subdivision of mathematical modeling. It explores the question of limiting convex set functions.
In more practical terms, convex optimization is a widely-used technique for modeling uncertainty and studying optimization problems that arise every day. By using the methods of convex optimization, we can solve linear and quadratic programs easily and efficiently. It can be used to figure out things like attainable performance.
Convex optimization solves problems using tools like bundle methods, subgradient projection, and ellipsoid methods. Anyone who uses computational geometry or squares linear and quadratic functions must know a little bit about it.
What Is Convex Optimization Used For?
Convex optimization is a versatile technique applied across a wide range of fields. It helps in formulating outcomes and in modeling large sets of data. Some of its applications are in these four areas.
- Signal processing. Convex Optimization is essential for processing signals. It is used to analyze, modify, and synthesize signals in the form of images, sounds, and scientific waves.
- Statistics and machine learning. Using linear programming, statisticians and mechanical engineers can apply convex optimization to interpret outcomes of a function or a code. Learning the fundamentals of machine learning is a great way to get to know convex optimization.
- Digital and analog circuit design. Convex optimization can be used to create and analyze digital as well as analog circuits. It helps engineers predict the voltage at every node or junction in a circuit, and to optimize the devices attached.
- Economics and finance. In the field of finance and econometrics, convex optimization is used to study financial models and functions. With geometric optimization methods, economists can convert such models into understandable forms.
Types of Convex Optimization
To have such a wide scope of application, convex optimization necessarily comprises a variety of techniques. The following are some of the techniques that convex optimization encompasses.
Least Squares
This method is a common technique in regression analysis to estimate the answer to over-calculated structures. It does so by limiting the number of remaining squares in the results of each equation.
Linear Programming
Also called linear optimization, linear programming is used to optimize a linear objective function. The technique is used to obtain the best result in a mathematical model. It is used in business, for example, to calculate maximum profit and minimum cost.
Convex Quadratic Limitation with Linear Constraints
A kind of non-linear data analysis, convex quadratic programming is used for solving mathematical optimization questions involving quadratic functions. It is especially useful for multivariable quadratic functions that are sensitive to linear variable restrictions.
Conic Optimization
This type concerns the optimization of convex functions over the junction of a convex cone and a convex subspace. Well-known categories of conic optimization problems include real vector spaces and real functions.
Geometric Programming
Geometric programming is similar to convex optimization. Simply by adjusting variables, every geometric program can be converted to a convex one.
This type of convex optimization has various applications, such as designing aircraft and maximizing probability calculations for logistic regression. It is also used in control theory to tune parameters for perfect positive models.
Semidefinite Programming
Semidefinite programming is a new subdivision of convex optimization. Many practical problems of optimization can be formulated or estimated as less defined programming problems.
Learning Convex Optimization
What it’s like to learn convex optimization will depend on your area of interest and how much practice you need to conduct certain techniques and tests. But when it comes to learning resources for convex optimization, there are multiple options to choose from.
We invite you to explore the online and physical learning resources listed below. With these at your side, all you will need is interest in the material and the motivation to get better.
How Long Does It Take to Learn Convex Optimization?
Depending on your level of interest, you can learn convex optimization by enrolling in a bachelor’s degree program or a master’s degree program. The latter option will take 20-36 months. Whether a master’s degree is worth your time depends on the structure of the program and your goals.
However, online courses and resources can also help you learn. With these, you can enhance your understanding in less than a week.
How to Learn Convex Optimization: Step-by-Step
Let’s break your journey down into five basic steps.
- Choose an online course or a training program. Decide between an online course or an in-person training program according to your preference. If you’re comfortable attending online classes, the primary option is to choose an online course.
- Get yourself enrolled. If you’ve decided to start learning convex optimization, don’t waste time. Enroll in a suitable course and start your learning journey. A good place to start is our list of the best courses available, which you can find down below.
- Learn algorithms. Computer programming and algorithms are how you implement convex optimization. You need to have a strong understanding of the fundamentals. This will help you better grasp the material covered in high-level courses.
- Increase your knowledge by reading books. Books will give you a head start when planning to learn something. Check the list below for our top recommendations.
- Learn statistical tools. Statistics enable better application of convex optimization. Statistical tools like regression and representation will be especially useful to learn.
The Best Convex Optimization Courses and Training Programs
University degree programs and courses are a great way to learn a skill. Before we get to the online courses, let’s take a look at two of the best on-campus options for learning convex optimization.
Charles University Faculty of Mathematics and Physics
- Name: Master in Discrete Models and Algorithms
- Time: 2 years
- Prerequisites: Bachelor’s degree
- Cost: $6,436
Located in Prague, Charles University offers a full-time master’s degree program. Students interested in convex optimization will learn about discrete mathematics and other optimization methods.
The course covers some of the most important mathematical concepts in computer science. It provides expert knowledge to students with an undergraduate degree in computer science or applied math.
Purdue University
- Name: Intro to Convex Optimization
- Time: 3 credit hours
- Prerequisites: Bachelor’s degree
- Cost: $40,000
This graduate-level course introduces students to the basics of convex analysis and convex optimization. It covers basic algorithms of convex optimization and applications in aerospace engineering. The semester ends with a big hands-on project.
Online Convex Optimization Courses
There are many online certification courses that you can take to learn convex optimization. better. Here are two of the best ones.
Harvard Extension School
- Name: Advanced Optimization
- Duration: Instructor-led and self-paced
- Prerequisites: Higher-level Mathematics
- Cost: $2,750
This course presents mathematical programming and combination optimization from the point of view of convex optimization. It teaches optimization as a fundamental technique for solving big problems.
One half of the course is devoted to the concept of convex optimization and its applications for machine learning, data analysis, and signal processing. The second section develops techniques from the first section to explain and illustrate more advanced combination optimization methods.
Udemy
- Course name: Optimization Problems And Algorithms
- Time: 8 hours
- Prerequisites: Basic knowledge of programming
- Cost: Varies
This course is an introduction to dynamic optimization problems and algorithms, which are the two key components of learning AI. You will cover the basic principles in the area of optimization. You will also learn about swarm intelligence. After completing this course, you will be able to identify and apply the key components of the optimization process.
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Many of the video lectures in this course involve coding. But don’t worry. The instructor will walk you through the process, step by step. And it includes multiple quizzes for you to practice your learning.
Free Convex Optimization Courses
In addition to the paid certification courses, here are some of the free courses offered by respectable institutions and vendors.
Stanford University (edX)
- Name: CVX101: Convex Optimization
- Duration: 8 weeks
- Prerequisites: None
- Cost: Free
This course focuses on the identification and resolution of convex optimization challenges that occur in applications. The curriculum includes convex sets, operations, optimization problems, the basics of convex analysis, and much more. You will especially benefit from this course if you are pursuing computer science engineering or a master’s in finance.
University of Melbourne (Coursera)
- Name: Discrete Optimization
- Duration: 8 weeks
- Prerequisites: None
- Cost: Free
This introductory course will teach you how to solve complex problems using discrete optimization principles and algorithms. It covers a wide range of techniques and applies them to real-world problems, such as issues in supply chain optimization.
Best Convex Optimization Books
Below are four of the best books on convex optimization, with brief summaries and Amazon ratings to go with each entry.
Convex Optimization, By Stephen Boyd and Lieven Vandenberghe
This detailed and practical introduction aims to identify convex optimization problems and find the most suitable method of solving them. It includes many examples and homework assignments. Students and researchers in the fields of computer science, math, statistics, economics, and finance will get a lot out of this book.
Convex Optimization Algorithms, By Dimitri P. Bertsekas
This book emerged out of Professor Bertsekas’ experience teaching in MIT classrooms over 15 years. With his combination of thorough mathematical analysis and clear description of concepts, Bertsekas offers an insightful window into how to solve real-world convex optimization problems.
Convex Analysis and Nonlinear Optimization, By Jonathan Borwein
This book delves into the theory behind modern computational optimization methods, but its main purpose is to provide a detailed, clear summary of convex analysis and its applications.
Each section ends with a wide variety of practice exercises.
With the perfect blend of theory and practice, Borwein and Lewis are able to illustrate why optimization is a rich and flourishing mathematical discipline.
Statistical Inference via Convex Optimization, By Anatoli Juditsky
Based on the latest research, this book explores why convex optimization is a valuable technique for statistical inference. It is recommended for data analysts who wish to develop their optimization techniques but is also accessible for beginners.
Among other topics, readers will learn how convex optimization theory is used to form and analyze near-optimal statistical problems.
Online Convex Optimization Resources
It’s not just online courses and books. The Internet has plenty of other resources to help you learn convex optimization. The resources featured below are free tools that you can use to enhance your understanding of the concepts.
YouTube
YouTube is a treasure trove of free tutorials. To learn about convex optimization and other topics in math and statistics, check out the channels of Ahmad Bazzi and Bob Trenwith.
Carnegie Mellon University: Statistics and Data Science
Originally posted by Ryan Tibshirani on the CMU website, this resource offers detailed slides, problem sets, and study guides for free. These materials clearly explain and demonstrate the fundamentals of convex optimization.
Should You Study Convex Optimization?
Convex modeling is an optimization technique with seemingly limitless applications. It is used to study set functions, to design computer algorithms, and has applications for signal processing, finance, and economics.
Knowing convex optimization will provide you with respectable career options. Engineers, researchers, and designers are just some of the professions that use convex optimization every day. If you want to stand out from the crowd and add meat to your resume, then you should learn convex optimization.
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