The weak duality theorem states that for any optimization problem, the value of the dual objective function is always less than or equal to the value of the primal objective function at any feasible solution. This principle highlights the relationship between primal and dual formulations, providing a way to assess the quality of solutions and bounds for optimal values. Understanding this theorem is crucial in applications like Lagrange multiplier theory and primal-dual interior point methods, as it establishes foundational insights into optimality conditions and solution methodologies.
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