AbstractDissonance
Reputation
390
Top tag
Next privilege 500 Rep.
Access review queues
 Jul2 awarded Curious Apr10 comment Divergence and curl united? @ZettaSuro Because the div and curl are defined at a point. C can be easily parameterized as dr and as dr->0 the circle gets smaller and smaller around the point in question. Apr10 asked Divergence and curl united? Apr9 asked Higher orders of divergence and curl Sep29 comment A chain 64 meters long whose mass is 20 kilograms is hanging over the edge of a tall building… Is all the 64 meters hanging over? It makes no sense how it is worded. If you list the top 3 meters you are just lifting the end of the chain. Also, are you pulling the entire chain up or just the end up? (they are different problems) Sep28 revised exp(ab) decomposition added 47 characters in body Sep28 comment exp(ab) decomposition @AndréNicolas heh, sorry too, I guess in my revision I deleted the part where I wanted c(x) to be independent of b(x) in some way. I'll update it to make it clear. Sep28 comment exp(ab) decomposition @AndréNicolas Did you not even bother to read the post? I said towards the end THAT IS NOT what I want! Sep28 asked exp(ab) decomposition Sep28 comment Joint/Simultaneous optimization Well,I have mentioned what I mean plenty of times. Ugly came from the |fg| example. Bad came from the "closeness" to the individual problems. You want me to give you exact meaning but I'm the one that asked the question. Essentially what it boils down to is categorization and I have categorized them informally... not much more I can do, else I wouldn't be asking the questions. It should be rather intuitive to you, though, that there is some partial ordering that exists. Sep27 comment Joint/Simultaneous optimization Just because some forms are not much different than others when it comes to the joint optimization problem does not prove that all forms are not much different. Again, I've already pointed out that $|fg|$ from your list of examples is bad and one case(and there are an infinite number). You need to look at the big picture and take the set of all "forms" and realize that some are truly "bad"... and I'm asking if there is a general way to "group" the good, bad, and ugly. (not necessarily a total order but a partial order) Sep27 comment Joint/Simultaneous optimization Again, your missing the point. SOME FORMS DO NOT WORK AT ALL! If that is the case, which it is as $|fg|$ proves this, then this means there are AT LEAST forms that are better than others. It may mean that there is a spectrum from good to bad. The whole point of the post was to find about how the "forms" fit into this "spectrum". Your getting hung up on trying to prove something equivalent that a saddle point doesn't have an extrema and missing the point that I'm trying to quantify the relationship between points near the saddle point and those that aren't. Sep27 comment Joint/Simultaneous optimization (BTW, x and y may not be comparable which is what you think your trying to get me to understand BUT z and x and z and y definitely are which is what I'm trying to get you to understand) Sep27 comment Joint/Simultaneous optimization YET, since z is much worse than x and y(say) THIS means there is some ordering that exists. It may not be well defined to some degree but in this case z < x and z < y. I've already pointed out that I want a joint minimization problem WHO's solution tries to minimize the individual minimization problems well. You've given a number of functional forms to represent the joint minimization as I have proven, some do a better job than others. Do you have any clue as to how to compare these functional forms to determine which ones do better a better job? Sep27 comment Joint/Simultaneous optimization But I'm trying to find joint minimization forms that produce good results for the individual cases. I've already point out that there are joint minimization problems that do not do this necessarily do this. HENCE, if not all joint minimization problems produce good individual results THEN that means some are better. Simple as that. I'm looking for some way to quantify what this behavior. E.g., you say x, y, and z are possible functional forms for joint minimization and I say: "z is not good to also produce good individual minimization results"... and you say "it's impossible to find one". Sep27 comment Joint/Simultaneous optimization No, You must be misunderstanding me. It is obvious the individual cases can be minimized as they are individual problems and they both have solutions. Surely you get that. argmin f(x) and argmin g(x) both have solutions(in general)... but are not related in any way. Now if we have some sort of joint minimization problem AND WE WANT for it also to try and do it's best to solve the individual problems THEN some functional forms are better than others. Your your to get across to me that there are many possible definitions of the joint minimization by itself. I know that. Sep27 comment Joint/Simultaneous optimization I think you mean something like $(1 + |f|)(1 + |g|)$ as the case still occurs with $1 + |fg|$. The issue comes from multiplication by 0 as 0 times anything is still 0. When I was looking into this I first thought of using the additive case f + g with f and g >= 0 but decided to use $|1 + f||1 + g|$ but I can't recall what the problem with addition was. I also "absorb" the weighting into the functions so $f^2 + a g^2 \equiv f^2 + g^2$. What would be nice to have is a joint function that can be proven to minimize the individual cases the best(if one exists) as that is what I'm looking for. Sep27 comment Joint/Simultaneous optimization @ChristianBlatter The issue is not so much about which is best but which will absolutely not work. Some interpretations of "joint minimization" simply make know sense and others seem to be preferred for a more general, unbiased case. The whole point of a joint minimization, I believe, is to minimize the individual cases well but leaving "wiggle" room. But the the solution will be worthless if the "wiggle" room is too great since it's solution will not work at all for the individual cases. Therefore, it seems having such an interpretation would limit possible choices for a joint function. Sep27 revised Joint/Simultaneous optimization added 1601 characters in body Sep27 comment Joint/Simultaneous optimization It seems, though, in some cases, it does not work well though: $\sqrt{|fg|}$ could allow for any possible h which gives f(h) = 0 but g(h) is $\infty$... which is obviously not minimizing g alone. I agree there are many different possible results but which ones can be proved to also minimize the individual minimization problems "well". e.g., maybe "$|f(h1) - f(h) + (g(h2) - g(h))|$" is small... would would then exclude $\sqrt{|fg|}$. (h1 and h2 would be the optimal solutions for the individual equations). Hopefully this makes some sense.