The interplay between optimization and machine learning is one of the most significant developments in modern computational science. Optimization formulations and algorithms play a central role in designing efficient methods for extracting meaningful structure and knowledge from large-scale data. Machine learning, however, is not merely a consumer of optimization techniques; it is a rapidly evolving field that both motivates and inspires new optimization models and algorithms capable of addressing the increasing complexity, scale, and diversity of modern data-driven systems.

This course is intended for mathematics students and others with a strong mathematical background. Its purpose is to present core optimization algorithms together with the theoretical principles that explain their effectiveness and convergence behavior, and to highlight recent advances in machine learning and deep learning that are guided and supported by optimization theory.

At the end of this course, the student will be able to:

• Understand the state of the art in the interaction between optimization and machine learning;

• Understand the optimization methods that form the foundation of modern machine learning algorithms used in real-world applications;

• Examine recent advances in machine learning that are driven or supported by optimization theory.