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Apr
14
comment Maximum translation distance between piecewise functions that satisfy a condition
If the details are hard to digest, perhaps you can propose values for $a,b,z$ and I can quickly show how to find $d$ to illustrate the use of the formulas.
Apr
13
revised Maximum translation distance between piecewise functions that satisfy a condition
minor edit, missing exponent -1 on D
Apr
13
revised Maximum translation distance between piecewise functions that satisfy a condition
added details on expressing the minimum value of F_total and computing D to get Z
Apr
13
comment Maximum translation distance between piecewise functions that satisfy a condition
I will fill in all the details.
Apr
9
revised Maximum translation distance between piecewise functions that satisfy a condition
outlined reduction to special case in greater detail, hinted at further development
Apr
8
answered Maximum translation distance between piecewise functions that satisfy a condition
Apr
8
comment Maximum translation distance between piecewise functions that satisfy a condition
That's very helpful. I think I have a good sense of what your goal is, and an idea at least how to get the maximum $d$ more quickly than just incrementing it by small amounts. To assure $f_{\text{total}}(x) \ge z$ we can start with $d = 2a/b$, where the overlap is just a single point, and the condition must fail (assuming $z \gt 0$). Then we can quickly cut $d$ in half repeatedly until the condition succeeds. Finally we have to narrow the search for the exact $d$ over the last "double" length. I'll outline this approach in greater detail.
Apr
7
comment Finding most efficient route (distance/number of nodes) that uses nodes at least X amount away from another node
Perhaps you are saying that any package can be dropped off anywhere, that the destination is not specified by the package being picked up?
Apr
7
comment Finding most efficient route (distance/number of nodes) that uses nodes at least X amount away from another node
It's unclear what you found to disagree with in what I wrote. I said "the number of package pickups is not constrained," and you write that there is "no upper or lower limit to the number of nodes". Your description of the perfect route being "one where the pickup and dropoff points are separated by the minimum distance possible" does not follow from the premises outlined in your post. So long as the entire route length is minimized for a given number of payoffs, it will not be suboptimal simply because some of the dropoffs take place over longer distances.
Apr
7
comment Finding most efficient route (distance/number of nodes) that uses nodes at least X amount away from another node
In particular the payoff depends only on whether the pickup and delivery points are at distance $X$ or more, and so one simply ignores the packages for which this is not true.
Apr
7
comment Finding most efficient route (distance/number of nodes) that uses nodes at least X amount away from another node
If I understand your question, the 3D "cloud" of points consists of some where there are packages to pick up and some where there are deliveries to be made. Supposing for the moment you have full knowledge of these opportunities, and that the capacity of the delivery vehicle is such that the number of package pickups is not constrained, you want to compute the shortest route to deliver all of them.
Apr
7
comment How to speed up fmincon in MATLAB when there are many variables? Alternatives to MATLAB optimization toolbox?
You are likely running afoul of "the curse of dimensionality", that with increasing numbers of variables the solution space undergoes "combinatorial explosion". However you need to explicitly pose your problem in order to get specific suggestions on how to cope.
Apr
7
reviewed Reviewed Minimizing quadratic form in Matlab
Apr
7
reviewed Approve Finding most efficient route (distance/number of nodes) that uses nodes at least X amount away from another node
Apr
6
comment Maximum translation distance between piecewise functions that satisfy a condition
I'm not sure how familiar you may be with the "hat" functions as a basis for piecewise linear functions, but your problem is new to me. With the so-called "hat functions" the basis is formed by translating one function a distance $d$ that is exactly half the (symmetrical) support size of that function, i.e. $d = a/b$ in your notation. Apparently you contemplate distances $d$ that are arbitrary proportions of that, so that your functions pack more closely together.
Apr
6
reviewed Approve Maximum translation distance between piecewise functions that satisfy a condition
Apr
6
reviewed Reviewed How to calculate grid coordinates of the centroid based on four attributes in a spider chart
Apr
6
comment How to calculate grid coordinates of the centroid based on four attributes in a spider chart
The title initially led me to think the problem was about calculating attributes, but reading through the post makes me think it is more about visualizing some known information. A naive approach would require four dimensions to display the four attributes, but I sense your desire is to find the best way to display information in two dimensions. Any way of doing this will involve loss of information for the most general data, but for a specific data set there will likely be a "projection" that minimizes the amount of information loss. Is this line of thought worth pursuing?
Apr
6
reviewed Reviewed How can I plot the Ramachandran regions in MatLab?
Apr
6
comment How can I plot the Ramachandran regions in MatLab?
I'm just musing as I don't have any familiarity with the plot command you mention, but perhaps the scatter plot could be more easily added to the shaded regions, rather than the other way round?