## convex optimization – min-max theorem proof, equivalence of duality problems, how does that work?

I try to prove the min-max theorem. In it, I have to prove the following equivalence of the linear program (one is the double of the other):

$$max {x_0 mid textbf {1} x_0 – A ^ T x leq 0, sum x_i = 1, x > geq 0 }.$$ $$iff$$

$$min {y_0 mid textbf {1} y_0 – A y geq 0, sum y_i = 1, y geq > 0 }.$$

How it goes ?

## Live cricket streaming site SE optimization required

Hi guys, I'm looking for suggestions related to the live cricket streaming site Search Engine Optimization.

I've done White Hat SEO, but I think I did not do it right due to time constraints and now I want suggestions from you guys. Please tell me.

Crichd live online (Sportschunky.com)

https://sportschunky.com/tv/crichd-live-cricket-streaming-free/

## Query Performance – SELECT optimization in Postgresql 10

I want to select the last unique lines based on the time.

    SELECT DISTINCT ON (title) *
FROM eco.tracks WHERE id> (SELECT id FROM eco.tracks WHERE time_track <((SELECT time_track FROM eco.tracks ORDER BY id DESC LIMIT 1) - INTERVAL & # 39; 300 seconds & # 39;) ORDER BY id DESC LIMIT 1 )
ORDER BY track, time_track DESC;


It gives me 20s, that's too slow.
If I replace ID with real value. it gives me 2ms

                    SELECT DISTINCT ON (title) *
FROM eco.tracks WHERE id> 48000000
ORDER BY track, time_track DESC;


This query

SELECT id FROM eco.tracks WHERE Time Track <((SELECT Time Track FROM eco.tracks ORDER BY id DESC LIMIT 1) - INTERVAL & # 39; 300 seconds & nds; ORDER BY id DESC LIMIT 1


only gives 2ms ..

What is wrong?!

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App Store Optimization for Apps or Games

Your supplier writes a quality app description for an app according to the best practice guidelines for optimizing the app store.

1 platform

2 keywords researched

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200 app description words

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You forward the following information to your responsible supplier:

, Selection of the phone for the opening scene

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6 screenshots of the app

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## Non-liner optimization of a family of functions

I would like to have tips on the following problem (solution methods, problem category, etc.).
The context is about the simultaneous registration of multiple images ($$n$$ images, $$f_ {i, j}$$ the function that maps coordinates $$(x_i, y_i)$$ to $$(x_j, y_j)$$,

To let $$f_ {i, j} ^ k (x, y)$$ a polynomial function of order $$k$$ from $$mathbb {R} ^ 2$$ to $$mathbb {R} ^ 2$$With $$i, j in [1, n]$$,

For example when $$k = 0$$Such functions can be expressed as $$f_ {i, j} ^ 0 (x, y) = (a_ {ij} ^ 0, a_ {ij} ^ 1)$$,
Or when $$k = 1$$: $$f_ {i, j} ^ 1 (x, y) = (a_ {ij} ^ 0 + b_ {ij} ^ 0 x + c_ {ij} ^ 0 y, a_ {ij} ^ 1 + b_ {ij} ^ 1 y + c_ {ij} ^ 1 y)$$,

Accepted $$k$$ is fixed, is waived in the following.

This family of functions should take into account as much as possible in terms of property: $$f_ {i, j} = f_ {i, k} (f_ {k, j})$$,

I want to use this property to reduce the number of unknowns and get robust estimates of the coefficients.
In addition, I have a large number of matches that can be expressed as such: $$v = f_ {i, j} (u)$$,

My problem is this: How can I calculate the functions robustly? $$f_ {1, i}$$ ?

If $$k = 0$$The problem is quite simple: $$f_ {i, j} = f_ {i, k} (f_ {k, j}) = f_ {i, k} + f_ {k, j}$$ so I can write an over-constrained linear system and solve it with a Moore-Penrose inverse or an algorithm like RANSAC.

If k = 1 or 2, I do not know exactly how to proceed. I think I could try to design a custom convergence scheme with a given order of equation resolution and some convergence iterations.

As an example, if I solve $$f_ {1,2}$$to get then $$f_ {1,3}$$ I can use my matches of the form $$v = f_ {1,3} (u)$$ but also the games like $$v = f_ {2,3} (u) => f_ {1,2} (v) = f_ {1,3} (u)$$

Thanks, Thomas

## Convex Optimization – How is this max-min target linearized or convexized?

I gave an objective function through

$$Underset {a, b} { max} hSpace {1mm} Underset {i, i = 1, cdots, M} { min} hSpace {1mm} frac {s_i (a, b) } {d_i}$$

Here, $$a$$ and $$b$$ are optimization variables. $$s_i$$are functions of these optimization variables.

are $$max min$$ Optimization target non-linear / non-convex?

If so, how can I linearize / convexify it?

## Optimization – Optimum implementation of an animation in UE4

We've already created a track spline animation for a tank, but it needs a lot of memory because it's implemented in a tick function. So every second has to be checked, but as you may know, it takes a lot of resources if there are more than 10 tanks.

I would like to ask if you have an optimal solution for this problem or are faced with such problems.

P.S. would be great if the solution would lie in blueprints.

Many Thanks!

## Performance Optimization – Generate a coefficient array from the general formula of the linear equation system

This is a problem that occurs when implementing the finite difference method (FDM).

Here is a toy example. Suppose we want to solve the boundary value problem (BVP).

$$y & # 39; & # 39; (x) = sin (x), y (0) = 0, y (1) = 0$$

eq = y & # 39; & # 39;[x] == Sin[x];
bc = {y[0] == 0, y[1] == 0};


With FDM we can then program as follows. First write down the corresponding difference formula:

Clear @ dx;
generalformula = (y[x + dx] - 2 years[x] + y[x - dx]) / dx ^ 2 == sin[x];


Then define the grid size and generate difference equations at each grid point:

Points = 25; domain = {0, 1};
dx = @@ domain / subtract (1 - points);
var = table[y[y[y[y[x], {x, ##, dx}]& @@ domain;
differenceeq = table[Generalformula{xDomäne[[Generalformula{xdomain[[allgemeineFormel{xDomäne[[generalformula{xdomain[[1]]+ dx, domain[[-1]]- dx, dx}]~ Join ~ bc;


Finally, solve the difference equations with z. NSolve:

Solrule = NSolve[differenceeq, var][[[[[1]]; // Absolute timing
(* {0.00462427, zero} *)


Incidentally, a comparison with the analytical solution:

asol = DSolveValue[{eq, bc}, y, x]
plot[asol[asol[asol[asol[x], {x, ##}, PlotRange -> All]~ Show ~
ListPlot[solrule[[All, -1]], DataRange -> {##}]& @@ domain


Alternatively, we can extract the coefficient array Differenzäq and solve it LinearSolveas in the document of CoefficientArrays, This approach is faster than the one used NSolve:

{barray, marray} = CoefficientArrays[differenceeq, var]; // Absolute timing
(* {0,000614324, zero} *)
sol = LinearSolve[marray // N, -barray]; // Absolute timing
(* {0,000488251, zero} *)


However, this is not the end. As already mentioned, we have generated a difference equation at every grid point and then extract the coefficient array from the symbol system in the code above. This procedure can be quite memory intensive and slow if Points is big. Is it possible to generate Barray and Marray directly from general formula and bc programmaticallyin a memorable and not so slow way?

If the above toy example is too simple to illustrate the underlying problem, the following is more complicated to solve the problem mentioned here:

r = 0.8; Glass = (1.45) 2; Air = 1; k = (2π) / 1.55;
n2 = (function[{x, y}, #] & @ (SimplifyPWToUnitStep @
PiecewiseExpand @ if[X^2+y^2[X^2+y^2[x^2+y^2[x^2+y^2<= r^2, glass, air]));
ClearAll[fw, bw, delta]
SetAttributes[#, HoldAll] & /@ {fw, bw};

fw@D[expr_, x_] :=
With[{Δ = delta@ToString@x},
Subtract @@ (expr /. {{x -> x + Δ}, {x -> x}}) / Δ]bw @ D[expr_, x_] : =
With[{Δ = delta@ToString@x},
Subtract @@ (expr /. {{x -> x}, {x -> x - Δ}})/Δ]

delta[a_ + b_] : = Delta @ a + Delta @ b
delta[k_. delta[_]]: = 0
degree = function[expr, fw@D[expr, #] & / @ {x, y}];
div = function[expr, Total@MapThread[bw@D@## &, {expr, {x, y}}]];
elst = e[#][x, y]    & /@ Offer[2];
discretelhs =
With[{N2=n2[{N2=n2[{n2=n2[{n2=n2[x, y]},
div @ grad @ elst + (n2 k ^ 2) elst - grad[div@elst - 1/n2 div[n2 elst]]];
Points = 100; L = 2; domain = {-L, L}; grid = array[# &, points, domain];
del = #[[2 ;; -2]]&;
delta["x"] = Delta["y"] = -Subtract @@ domain / (points - 1);
vare = Outer[e[e[e[e[#][#2, #3]    &, Area @ 2, del @ grid, del @ grid, 1]// flattening;
discretelhslst =
Flattening when transposing[
Block[{e}, e[i_][L | -L, _]    = e[i_][_, L | -L]    = 0;
table[discretelhs, {x, del@grid}, {y, del@grid}]], {2, 3, 1}]; // Absolute timing
{barray2, marray2} = CoefficientArrays[discretelhslst // N, vare // N]; // Absolute timing
{val, vec} =
Eigensystem[marray2, -6,
Method -> {"Arnoldi", "Shift" -> k^2 glass}]; // Absolute timing
mat = ArrayReshape[#, {2, points - 2, points - 2}] & / @ vec;
MapThread[ArrayPlot[#[[ArrayPlot[#[[ArrayPlot[#[[ArrayPlot[#[[1]], PlotLabel -> Sqrt @ # 2, PlotRange -> All,


ByteCount[marray2]/ 1024 ^ 2. "MB"
(* 2.76122 "MB" *)

ByteCount[discretelhslst]/ 1024 ^ 2. "MB"
(* 180,695 "MB" *)


The corresponding problem is how to arrive marray2 from discreet and e[i_][L | -L, _] = e[i_][_, L | -L] = 0; without generating discreet` efficient enough?

## Variable in the exponent in an optimization problem

I have the following problem plugged

Minimize[{X^zz>=1z[{X^zz>=1z[{x^zz>=1z[{x^zz>=1z<= 10, x >= 1}, {x, z}]

Can someone please explain why the software does not offer the solution? The solution is clear $$x = 1$$ and $$1 leq z leq10$$,

## Optimization – Is the problem of the traveling salesman with the dikstra algorithm the optimal solution?

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