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The image is a geometric illustration related to the strong duality proof in convex optimization. It depicts two convex sets, \( A \) and \( B \), which do not intersect. The set \( A \) is shaded and located in the upper right quadrant, while \( B \) is positioned below the horizontal axis. The point \((\tilde{u}, \tilde{t})\) is marked within set \( A \). 

A line separates the two sets, demonstrating that they can be divided by a hyperplane due to their convex nature. The illustration supports the concept that, under Slater's constraint qualification, any separating hyperplane must be nonvertical. The axes are labeled \( u \) (horizontal) and \( t \) (vertical).

The text below the image explains the context of the illustration in relation to the strong duality proof and Slater’s constraint qualification. The slide is from A. d’Aspremont's "Convex Optimization M2" presentation, slide 45 of 49.
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