Advanced Algorithms in Continuous Optimization

Catalog description

The field of continuous optimization lies at the intersection of applied mathematics, operations research, and a wide range of scientific and engineering applications. In recent years, the rapid growth of data-driven technologies and large-scale computational models has led to intense research activity in the development and analysis of efficient optimization algorithms. Significant progress has been made in convex optimization, with mature theory and scalable algorithms now available. However, many modern applications arising in machine learning, signal and image processing, data science, and engineering design lead to inherently nonconvex optimization problems. For such problems, algorithmic design is considerably more challenging, and theoretical understanding is far less complete. This course focuses on algorithms for continuous optimization, with an emphasis on both convex and nonconvex settings. We will study a mixture of classical foundational methods and recent algorithmic developments that are widely used in contemporary applications.