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I have two optimization problems to solve simultaneously.

The problems are

$$\max_{x}xF(a-x+y)$$ and $$\max_y yF(b-y+x)$$.

Here, $a$ and $b$ are scalars and $F$ is a cdf. Is there any technique or easy way that I can use to solve for a solution $(x,y)$?

Andeanlll
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  • It's not clear what you mean by "solve simultaneously". Are you hoping for an $(x,y)$ pair that will simultaneously maximize both objective functions? Are you hoping for some tradeoff between them? Is multi-objective optimization the sort of approach you are looking for? – LarrySnyder610 May 23 '19 at 12:25
  • Also I'll just note, although it's probably clear already, that your functions are nonconvex, so that may add to your headaches, depending on what you are trying to do. – LarrySnyder610 May 23 '19 at 12:26

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