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Jul 26, 2023 at 20:45 comment added user_lambda Yes, sorry I didn't know about the proper etiquette regarding cross-posting. I'll make sure to cross-reference in the future.
Jul 26, 2023 at 20:40 comment added fedja @user_lambda You are welcome! The moral of the story is "Always ask exactly what you are interested in and let other people generalize if they find it appropriate". Another thing I noticed is that you have also made an identical post on MSE without cross-referencing. By the local etiquette, it is a "no-no" but I didn't want to talk about the written and unwritten rules before dealing with the question to your satisfaction ;-)
Jul 26, 2023 at 20:28 comment added user_lambda That's great! Thanks so much for your work on this!
Jul 26, 2023 at 20:27 vote accept user_lambda
Jul 26, 2023 at 20:01 comment added fedja @user_lambda Then, unless I misunderstood you somewhere, you are in good shape. See my last edit :-)
Jul 26, 2023 at 20:00 history edited fedja CC BY-SA 4.0
added 941 characters in body
Jul 26, 2023 at 19:34 comment added user_lambda That's right. Although if adding restrictions on $F_i$ helps, that would also be interesting.
Jul 26, 2023 at 19:31 comment added fedja @user_lambda And you still want the entries of $x$ to be non-negative, but the entries of PD matrices $F_i$ are unrestricted, right?
Jul 26, 2023 at 18:53 comment added user_lambda Thanks that's very helpful. I've edited the question to add specific expressions for $A$ and $b$.
Jul 26, 2023 at 17:54 comment added fedja @user_lambda Still "Not necessarily". Your only hope is some extra properties of $A$ and $b$, so what can you say about them?
Jul 26, 2023 at 17:53 history edited fedja CC BY-SA 4.0
added 602 characters in body
Jul 26, 2023 at 14:43 comment added user_lambda Thanks for your comment. I have added more information about my particular case.
Jul 26, 2023 at 13:34 history answered fedja CC BY-SA 4.0