Weak duality is a fundamental concept in optimization that establishes a relationship between the primal and dual problems, stating that the optimal value of the dual problem provides a lower bound on the optimal value of the primal problem. This means that if you have a feasible solution for the dual, its objective value will never exceed that of any feasible solution for the primal. It connects to various optimality conditions, Lagrangian duality, and further distinguishes between weak and strong duality in optimization theory.
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