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real analysis - The relationship between minimum of summation and the . . . I would like to investigate the relationship between: min{f(x) + g(x)} min {f (x) + g (x)} and min{f(x)} + min{g(x)} min {f (x)} + min {g (x)} I think that it is fundamental and of course there exists a theorem or a lemma handling this relationship but I cannot find out My try: I made a toy example: f(x) =x2 − 2x − 3 f (x) = x 2 − 2 x − 3 and g(x) = x2 + 2x − 3 g (x) = x 2 + 2 x −
What does min max in optimization problems mean? What if the places are swapped, or some other combination? maxB minA max B min A Finally, can the min-max prefix appear for any sort of optimization problem, i e quadratic programming (convex optimization), linear programming, dynamic programming? How does it differ from "minimax"?
How to covert min min problem to linear programming problem? The source of nonlinearity here is the inner min To reformulate it to a linear form, you need to replace that inner min For this purpose, you can define a new variable Ai A i equal to the inner min and substitute it i e replace Ai =mink∈KBk i A i = min k ∈ K B i k Next you need to insert a set of linear constraints to guarantee that Ai A i is actually the min of Bki B i k