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Mar 3, 2023 at 10:46 comment added მამუკა ჯიბლაძე I don't understand. When $M=J+1$, with your last formulation you get$$loss[q]=(v-CAP)q^M+(CAP-Mv+JC)q-J(C-v),$$for $v=CAP$ it is linear in $q$ with negative coefficient at $q$, so will attain lowest value at $q=1$. This function only has a global minimum strictly inside $(0,1)$ for $v>CAP$.
Jan 26, 2021 at 13:51 history edited Silvester CC BY-SA 4.0
reformatted equations
Jan 26, 2021 at 13:45 history edited Silvester CC BY-SA 4.0
added 4 characters in body
Jan 26, 2021 at 11:41 history answered Silvester CC BY-SA 4.0