Mathematics for Machine Learning and Data Science: Optimization with Mathematica Applications

TL;DR

This monograph explores mathematical optimization techniques relevant to machine learning and data science, emphasizing algorithms implemented in Mathematica for clarity and practical application.

Contribution

It introduces 27 Mathematica functions for optimization algorithms, demonstrating their implementation and application in a human-readable, accessible manner.

Findings

Development of 27 Mathematica functions for optimization

Algorithms cover linear, convex, and nonlinear optimization

Code examples illustrate practical use cases

Abstract

The field of optimization has gotten a lot of interest in recent years owing to significant advances in computer technology. Numerous issues in machine learning, economics, finance, geophysics, molecular modeling, computational systems biology, operations research, and all areas of engineering are now being resolved owing to the rapid growth of optimization methods and algorithms. This monograph presents the main theorems in linear algebra, convex sets, convex functions, single variable optimization, multivariable optimization, and their corresponding algorithms. We also briefly touch upon the constrained nonlinear optimization. We have found the Wolfram language to be ideal for specifying algorithms in human readable form. To minimize nonlinear objective functions, we have created 27 Mathematica functions that follow the principles of 18 algorithms. The code examples were carefully designed to demonstrate the purpose of given algorithm. The code for each algorithm will run as is with no code from prior algorithms or third parties required beyond the installation of Mathematica.