Optimization is the act of selecting the best possible option to solve a mathematical problem when choosing from a set of variables. The concept of optimization has existed in mathematics for centuries, but in more recent times, scientists have discovered that other scientific disciplines have common elements, so the idea of optimization has carried over into other areas of study from engineering to economics to physics to biology. Optimization seeks to discover the maximum or minimum of a function to best solve a problem. It involves variables, constraints, and the objective function, or the goal that drives the solution to the problem. For example, in physics, an optimization problem might seek to discover the minimum amount of energy needed to achieve a certain objective. The advent of sophisticated computers has allowed mathematicians to achieve optimization more accurately across a wide range of functions and problems.‎

Optimization helps data scientists and computer systems process data more effectively, estimate how many resources it will take to solve a problem, and search for the best solution based on the data available. These features make optimization a key tool that can help those who collect and analyze data. The methods of optimization work hand in hand with statistics and linear algebra to help you understand and process large amounts of data. Solving complex problems that rely on data becomes much easier when you apply the methods and formulas of optimization to them, which makes it essential for machine learning. In fact, today's computer science relies heavily on the relationship between machine learning and optimization. The principles of optimization apply in a different way in business, because nearly every business decision centers on maximizing or minimizing various factors and outcomes.‎

When you study optimization with online courses on Coursera, you can gain a broad base of knowledge as well as applications that allow you to put what you learn into practice. Beginning courses include those in which you learn the basics of optimization, whereas more advanced courses go deeper into topics like stochastic processes, machine learning through specific applications, or how to estimate financial models.‎