Lagrange duality is a concept in optimization that establishes a relationship between a primal problem and its dual problem, enabling insights into the original problem's solution through its dual. By forming the Lagrangian function, which incorporates constraints into the objective function, this approach allows for the analysis of optimality conditions and sensitivity. In both infinite-dimensional spaces and stochastic optimization, Lagrange duality plays a crucial role in determining solutions, offering computational advantages and theoretical insights.
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