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)
SEMrush

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?!

Selling – Search engine optimization for apps – Earn $ 300 a day – easy

HOW IT WORKS

No headaches, the services offered on the website are completely outsourced. The sale of this website includes all supplier data, including replacement suppliers.

In this multi-million dollar niche of mobile app optimization, anyone can run this business without the need for design, optimization, video production, or sales experience to run their own mobile app optimization business.

What happens when a sale takes place?

You will immediately receive an e-mail and a payment via PayPal when a customer places an order on your new website. Then you give the same order to the supplier to provide the required service.

You provide the supplier with the necessary information that you have already received from your customer, who has filled in this information in the order form. Your supplier will take over the provision of the service immediately, and you can inform your customer about the completion of the order.

Package 1

COST 5 $

SELL $ 59

YOUR PROFIT $ 54

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

2 competitors researched

200 app description words

Package 2

COST $ 20

SELL $ 99

WIN $ 79

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

4 keywords researched

4 competitors researched

400 app description words

Package 3

Video advertising package

COST $ 15

SELL $ 129

GAIN $ 114

You forward the following information to your responsible supplier:

, Selection of the phone for the opening scene

, Background color

, App name and symbol / logo in PNG format

, App description and text

, App Screenshots (6 screenshots required)

Your dedicated supplier creates a customized video:

30 seconds duration

6 screenshots of the app

6 text description (each text has a title and description)

Free selectable color

Background music

Custom model (Android or IOS)

Full HD 1920 * 1080 and 1080p

Package 4

Video advertising package

COST $ 29

SELL $ 159

YOUR PROFIT $ 130

You forward the following information to your responsible supplier:

, Selection of the phone for the opening scene

, Background color

, App name and symbol / logo in PNG format

, App description and text

, App Screenshots (6 screenshots required)

Your dedicated supplier creates a customized video:

Duration 60 seconds

6 screenshots of the app

6 text description (each text has a title and description)

Free selectable color

Background music

Custom model (Android or IOS)

Full HD 4k

Note: When you start processing many orders, you can enter into a relationship with multiple suppliers, which is continuously agreed in terms of price and delivery time, depending on the customer. You can also expand the range of services you need to upsell an inch of work.

Very reliable supplier with a proven track record. Including backup suppliers.

This site will run on autopilot if you have adequate communication skills. No telephone contact with customers is required. Forward emails only. No Skype calls, just e-mail exchange.

Keep in mind that you receive multiple orders for multiple mobile apps from the SAME CUSTOMER and referral business. So, the income of 10 customers per week could quickly double from $ 1,300 to $ 2,600 per week, based on the repeat and referral business.

Why is app optimization relevant to the current market?

In today's market, more than 60% of apps are discovered through the search on the App Store. Optimized keywords and highly-up-to-date visual elements such as app icons, screenshots, banners, and app preview videos, along with the right localization and high-quality PR backlinks, will help you find your audience because of an improved search presence.

App Store Optimization (ASO) has become an important marketing channel for mobile apps on Google Play and the IOS App Store.

ASO techniques take into account the value and volume of different keywords. If you select the wrong keywords, your app can become virtually undetectable. The optimization has three effects: maximum download, maximum yield, and maximum resale value. Many customers will be looking for an advertising and optimization phase after selling apps – which can bring enormous profits.

A professionally produced promo video is the key to highlighting and increasing the organic traffic on the download page of your app. A clever app promotion video also has great ASO benefits, meaning you can improve your app rank in the App Store or the Google Play Store.

Videos are powerful enough to relay messages to the target market. Most importantly; User acquisition, acquisition ratios and transaction volumes can skyrocket thanks to video. This is where your new business comes in … The market is still in its infancy!

Digital marketing will eventually rely solely on apps that work on a mobile phone operating system that will be iOS or Android!

How will it work again?

1. You buy this reseller site

2. You apply it with the simple marketing plan I provide (that works).

3. Receive requests that are easy to manage as all information requested by the prospect is easily listed on the order forms on the website.

4. The customer is impressed … then he makes a purchase via PayPal and you will receive the money immediately on your PayPal account, eg. $ 159 for package 4.

5. Then contact your supplier by e-mail with the order data filled out by your customer.

6. The supplier then delivers the project via e-mail and you simply forward this e-mail to your customer.

Most importantly, your supplier provides this service quickly and efficiently. Your customer expects to have 7 days before their order is processed, so they'll be overwhelmed by what they paid for by receiving their app optimization within an average of 2 days.

What do you get when you buy this site?

Premium Domain Name

Premium Design
SEMrush

marketing plan

Social Media Marketing Guide

Operation Manual

supplier contacts

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

Enter image description here

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}, #] & @ (Simplify`PWToUnitStep @
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,
ColorFunction -> "AvocadoColors"]&, {mat, val}]

Enter image description here

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?

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

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