Strong duality is a principle in optimization that states if a primal problem has an optimal solution, then its dual problem also has an optimal solution, and the optimal values of both problems are equal. This principle is especially relevant in convex optimization, where strong duality guarantees that solving either the primal or dual problem yields the same optimal result. Understanding strong duality is crucial because it connects various concepts such as optimality conditions, Lagrangian duality, and the nature of duality gaps.
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