duality in linear programming

Duality in linear programming refers to the relationship between two interconnected problems: the original (primal) problem, which seeks to maximize or minimize a certain objective, and its associated dual problem, which essentially assesses the value of the constraints. Solving one provides insights into the other, often making complex problems easier to analyze or verify solutions. The key idea is that the optimal values of the primal and dual problems are closely linked; under certain conditions, they are equal. This duality helps in understanding the limits of solutions and in designing efficient algorithms.