Convex optimization is a subfield of mathematical optimization that focuses on the theory and algorithms for minimizing convex functions or maximizing concave functions over convex sets. This academic concept investigates problems where any local optimum is also a global optimum, a property that makes these problems significantly more tractable and efficiently solvable compared to general non-convex optimization problems. Its significance lies in providing a powerful framework with provable guarantees for solving a wide range of problems across engineering, economics, statistics, and computer science.