minimize – Minimization of a very simple polynomial

The primary difference between case 1 and case 3 is that the former is a polynomial, whereas the latter is not.

As per Mathematica documentation for Minimize, if the function to be minimzed and the constraints (if any) for minimization happen to be polynomials, then Minimze would give us the global minimum. A quick 3D plot for 1 reveals that it has no global minimum, which explains why Minimze demonstrates the behaviour it does.

Plot for 1, both x and y run from -1000 to 1000

In fact, 1 describes a saddle surface.

In case of 3, however, it can be clearly understood that the function descends from $infty$ as Abs(x) grows larger, on either side of the $y$-axis, and as Abs(x) $ rightarrow infty $ on either side, y $ rightarrow 0 $ asymptotically. There’s no global minimum again, in-fact, no stationary points at all (contrast this with saddle/inflection points of a curve, where the univariate function is stationary, even if it’s not an extremum).

So, in both cases, the output obtained is what one should expect, going by the behaviour of the function, and the Mathematica documentation for Minimize.

regression – How to find optimal function to minimize the distance to a set of points

I’ve been working on a side project and I had to gather some data to look for a pattern. I need to find the optimal function that minimizes the Y distance for all the points in the dataset, and so far I used Geogebra to generate both a Polynomial Regression (degree 4) and a Linear Regression. However, I’m not positive whether using regression is the correct/best way to do so, as I’ve never worked with them.

The function I ended up using is a mix of both of them (for x <= 80, polynomial regression, else, linear regression).

This is what the graph looks like (note: only the blue points are counted, the other ones are older/not accurate)

Is there any better way to optimize this function or any other method I could use to achieve better results?

algorithms – Minimize the sum of diameters of 2-clustering graph

Are there an algorithm that for given weighted graph $G$, partition it into 2 cluster $C_1,C_2$ such that sum of diameters of two clusters minimized?

I find a paper with title

“C. Monma and S. Suri, Partitioning points and graphs to minimize the maximum or the sum of
diameters”

in some related papers but i can’t access to above paper to find out their’s algorithm. The above paper solve my problem in $O(n^2)$.

graphs – How to match two point sets to minimize total distance?

Let’s say we have two sets $X = {x_1, ldots, x_n} subset mathbb R^d$, $Y ={y_1,ldots, y_n} subset mathbb R^d$, how can we find a permutation $pi$ such that

$$D = sum_{i=1}^n d(x_i, y_{pi(i)})$$

wis minimal? (Here $d$ is some distance function, for simplicity we can assume it is the Euclidean distance, or maybe the squared euclidean distance.)

As far as I remember this is a well studied problem, but can anyone tell me what it is called?

c# – Better way to minimize array elements

I would like the array elements to minimize by preserving their orders. For example,
3,7,9,7 is given 1,2,3,2 is yielded. 1,99,90,95,99 is given 1,4,2,3,4 is yielded. Think array can be ranged btw 1 to 100, exclusively. My try’s time complexity is (n^3)+n. Can there be more efficient way to solve this?

int() arr = new int() {2,5,3,5}; // example input


var copy = (int())arr.Clone();
var num = 101;
foreach(var x in arr)
{
    var min = copy.Min();
    for(int i = 0 ; i < arr.Length; i++)
    if(min == arr(i))
    {
        copy(i) = num;
    }
    num++;
}

for (int i = 0; i < copy.Length; i++)
{
    copy(i) = copy(i) % 100;
}

polynomials – How to minimize this function of two variables

I’m trying to minimize this function of $s$ over some bounds of $x$ and $y$.
The function is
$$frac{s x y + 1}{a b s^{3} x y + a s^{2} left(b + xright) + s x y + 1}$$
$a$ and $b$ are constants, and I am chiefly concerned about the minimization over some range of $s$, which happens to be a few orders of magnitude.
How would I classify this type of optimization? Is there any python scipy capability to solve it? scipy.optimize.minimize can’t seem to handle the range of s.
For context, this is the Laplace Transform representation of an electrical circuit.

Keep windows maximized after you minimize and alt-tab to them

Following these steps:

  1. Open a window and maximize it.
  2. Minimize it (so you end up on Desktop).
  3. Alt-tab back to it.

The window doesn’t restore to maximized state, but ends up in the “restored down” state or whatever it is called (halfway between minimized and maximized).

In Windows 7 it always restored to maximized state. Can we set this behavior in Windows 10?

c# – How does Adobe Photoshop have custom close, maximize, and minimize buttons on Windows 10? What language or framework does it use?

I am getting into desktop programming and I want to know which language/framework should I use for windows desktop programming. For macOS, I have decided on Swift and for Linux, Java + JavaFX. But for windows, I can’t pick between C++/WinRT + Win32 or C# with UWP (mostly, a bit of WPF). I already have basic knowledge of C# + XMAL and I am also fine with working hard learning C++. My main concern (at this moment) is that with UWP, I cannot create my own custom close, maximize, and minimize buttons like Adobe Photoshop has (see screenshot below). Their title bar is also thinner than other apps. What do they use? What would you recommend?

enter image description here

Thanks!

How can we Minimize Business Costs and Risks ?

Reducing cost is the main challenges in our own business. Lots of ways we can reduce our business cost. I mention some point…

1.Establish a workplace-safety training program for employees

2.Place injured employees who qualify on a modified work plan

3.Conduct background checks on new employees

4.Enforce a drug-free workplace

5.Hire an outsourcing partner to handle workers compensation issues