Starter — Convex Optimization

Convex Optimization is the foundation of foundations!

This chapter provides a concise introduction to foundational concepts in convex optimization, including convex sets and functions, Fenchel conjugates, Lagrangian duality, and the Karush-Kuhn-Tucker (KKT) conditions. Definitions are accompanied by illustrative examples to build intuition and support practical understanding. While convex optimization is a rich and expansive subject that merits its own dedicated volume, our focus is intentionally selective. We present only the essential tools and results that the author considers most relevant for understanding and analyzing optimization problems encountered in later chapters. The goal is to equip readers with a practical yet rigorous foundation, enabling them to appreciate the theoretical underpinnings of algorithm design and analysis in subsequent chapters.

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