weak duality

Weak duality is a fundamental concept in optimization that states the value of any feasible solution to a problem's "dual" (a related, derived problem) provides a bound on the original ("primal") problem. Specifically, for minimization problems, the optimal dual solution's value is always greater than or equal to the optimal primal value. This means the dual problem offers a way to estimate the best possible outcome of the original problem from above, ensuring that solutions are bounded and helping verify the quality of approximate solutions or bounds without needing to find the exact solution.