Constrained optimization is a mathematical method used to find the best possible solution to a problem while adhering to specific limitations or constraints. These constraints can be in the form of equations or inequalities that define the boundaries within which the solution must lie. This approach is commonly applied in various fields, including economics, engineering, and operations research. In constrained optimization, the goal is typically to maximize or minimize an objective function, which represents the outcome of interest. Techniques such as the Lagrange multiplier method are often employed to handle the constraints effectively, allowing for a systematic way to explore feasible solutions while ensuring that all conditions are satisfied.