Optimization theory is a branch of mathematics and economics that focuses on finding the best solution or outcome from a set of possible choices. It involves maximizing or minimizing a particular function, often subject to certain constraints. This theory is widely used in various fields, including engineering, finance, and operations research, to improve efficiency and decision-making. The core concept of optimization involves identifying the optimal values of variables that yield the best results. Techniques such as linear programming, integer programming, and dynamic programming are commonly employed to solve optimization problems. These methods help in making informed decisions by analyzing trade-offs and resource allocation effectively.