multivariable calculus - Geometric interpretation of duality and Slater's condition - Mathematics Stack Exchange

I am trying to study about optimization problems, Lagrange duality and related topics. I came across some presentation on the net, which claims to show the geometric interpretation of the duality and

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Please explain the intuition behind the dual problem in optimization. - Mathematics Stack Exchange

Hierarchical distributed optimization of constraint-coupled convex and mixed-integer programs using approximations of the dual function - ScienceDirect

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