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What does $\max_{i=1}^k (f_i(x) - q_i)$ mean?

Is it a sum?

This is the Chebyshev achievement function. And it's taken in "$L^{\infty}$ sense".

The optimization problem related to this is written:

$$\min_{x \in S}\max_{i=1}^k (f_i(x) - q_i) $$

Does this mean that one finds first index $i$ or $x$?

mavavilj
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    The context might give more information. At first glance, this is the maximum of $f_1(x)-q_1, \dots, f_k(x)-q_k$ where $x$ is fixed and the $f_i$ taking values in an ordered set. – mathcounterexamples.net Feb 20 '19 at 18:35
  • @mathcounterexamples.net Yes, I think it's the same as "sup-norm". However, I also put an extra question w.r.t. how to read this when in an minimization problem. – mavavilj Feb 20 '19 at 19:00

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