Is there an intuitive way to understand the convex duality? If the primal problem is minimization, the dual is maximization over another set of variables - but I would love to have a geometric visualization of this and an intuitive way to understand why this ought to be true. I'd also want to see strong duality present in such an intuition.
Textbooks are dense in the math, but I haven't come across a place where this could be imagined in our minds without variables and equations. Could someone here help me out?