oc.optimization and control – First Order Conditions concave optimization problem

I am self-studying optimization and I came across the following problem in an example

$$begin{array}{rl}max_{w,z} & z quad text { s.t.} \ f_{j}left(w_{1}, w_{j}right)-z & geq 0, quad(2 leq j leq N)end{array} \begin{aligned} sum_{i=1}^{N} w_{i} &=1 \ w_{j} & geq 0 quad(2 leq j leq N) end{aligned}$$

where $f_j$ are concave functions.

The First Order Condition provided in the solution for the optimal point $w_j^*$ are the following:

$$begin{aligned} 1-sum_{j=2}^{N} lambda_{j} &=0 \ lambda_{j} frac{partial f_{j}left(w_{1}^{*}, w_{j}^{*}right)}{partial w_{j}} &=gamma quad j=2, ldots, N end{aligned}$$

$$sum_{j=2}^{N} lambda_{j} frac{partial f_{j}left(w_{1}^{*}, w_{j}^{*}right)}{partial w_{1}}=gamma \
lambda_{j}left(f_{j}left(w_{1}^{*}, w_{j}^{*}right)-zright)=0 quad j=2, ldots, N$$

for some $gamma,lambda_j$, for $jin(N)$.

Can someone explain how these conditions are derived or point out some reference from which I could derive these? Thanks a lot

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optimization – Can LASSO algorithm solve for sparse $w$ in an under-determined system?

Consider the model $bf y=Xw+n$ where $bf w$ is a sparse complex number vector of length p, X is a N x p known complex number matrix, and $bf n$ is a complex Gaussian noise.
I’m confused because the literate answers yes to my question (in the title), but when implementing most of the functions provided in:
https://www.cs.ubc.ca/~schmidtm/Software/lasso.html
I get invalid solution.

Is LASSO supposed to solve an under-determined system?

mathematical optimization – NMinimize returns “Function is not a number at …”

I am currently trying to minimize MSE between two sets of data, using NMinimize. One of the question threads here offered a solution to use Method -> "RandomSearch to potentially avoid local minimum trap, and setting MaxIterations allows me to save some time, even tho this code runs for almost 4 hours.

Below is my running code,

    Timing(
 NMinimize({(Sum((Re(GenericFunction(ptstry((i)), r, s)) - nums((i, 2)))^2,
      {i, 1, Length(nums)}))/Length(nums),
   rUpper >= r >= rLower, sUpper >= s >= sLower}, {r, s},
  Method -> "RandomSearch",
  MaxIterations -> 10^2)
 )

and the return is below,

NMinimize::nnum: The function value 1/304 (2558.86 +(-1.10968+Re({0,1,2,3,4}.Re(PDF(<<2>>))/(1+Times(<<2>>))))^2+(-1.13174+Re({0,1,2,3,4}.Re(PDF(<<2>>))/(1+Times(<<2>>))))^2+(-1.05333+Re({0,1,2,3,4}.Re(PDF(<<2>>))/(1+Times(<<2>>))))^2+(-1.08594+Re({0,1,2,3,4}.Re(PDF(<<2>>))/(1+Times(<<2>>))))^2+(-1.06962+Re({0,1,2,3,4}.Re(PDF(<<2>>))/(1+Times(<<2>>))))^2) is not a number at {r,s} = {9.91862,8.48582}.

I have checked couple of questions on mathematica stack exchange but none of the solutions/tips helped me with my problem.

I was wondering if either my code is wrong somewhere, or the function GenericFunction is causing me problems. GenericFunction is calculated using the stationary distribution of a DiscreteMarkovProcess. I can provide more details on the GenericFunction if needed.

PS: I had to change some of the names in the code, so if there is a nameing mismatch do not mind that.

oc.optimization and control – How to solve this non-continuous optimization problem?

I hope you are well. I have a non-continuous optimization problem as follows;

  *The Goal: max ∑i lotsize(i).(35f(i)-30)
  Constraits: lotsize(i) >=0.1,
              lotsize(i) is not continuous.*

where i represents ith trade , f(i) function is as follows;

          *f(i)= 1  ; if a trade is successfull,
                0  ; if a trade is not successfull.*

I try to create a lotsize function. So, I wonder if there are any ways to obtain lotsize function from the aboved optimization problem.

Thanks for your help!
Best,

Murat Y.

nonlinear optimization – Gradient of the function in the BFGS Quasi-Newton Algorithm

I have a function $f=sumlimits_{k=1}^{K}|R_{k}^{dl}- R_{k}^{ul}|$ that I want to minimize using the BFGS Quasi-Newton algorithm.

If $R_{k}^{dl} = y_k times A times B times C$.

$y_k$ and $R_k^{ul}~ forall~ k in {1, 2, dots, K}$ are given.

Also, $A$ is given, $B$ is not given, and $C$ is a function of $B$ only.

If I want to calculate to the gradient of the function ($nabla f$). Should I calculate it with respect to all variables or with respect to $B$ only?

What’s the difference between landing page optimization and conversion rate optimization? – SEO Help (General Chat)

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seo – Question on search engine optimization for nodejs website

It’s true that this makes your content not indexable.

The general solution for this is to design a system for deep linking, where someone can share a link to a specific resource on your website (this could even just be a query string), and that resource loads immediately without any user interaction.

For instance, a link like this that opens up your map to a specific piece of content:

http://example.com/map.php?location=1234

Then, the trick is to surface those deep links somewhere so crawlers will stumble upon them. People will naturally surface them by linking in to your site from other sites, but you may want to create something like a “featured locations” page or blog about it to create more deep links for the crawlers.

Another idea: From each location deep link, you could also deep-link nearby locations or related locations, so the crawlers can start to traverse your locations sort of like linked pages.

Some people might suggest just slapping all your deep links into a sitemap and calling it a day, but there are probably issues with that.

c# – Entity Framework optimization when using transactions

I want to save NUnit local tests in a mysql database hosted in Amazon RDS, and

I’m wrapping up everything in a transaction like so :

using (var context = new StDbContext())
         {
            context.Database.Log = Console.Write;
            if (!context.Database.Connection.State.HasFlag(ConnectionState.Open))
            {
               context.Database.Connection.OpenAsync();
            }
            using (var transaction = context.Database.BeginTransaction())
            {
               try
               {
                  var unit_of_work = new UnitOfWork(context);
                  unit_of_work.Sessions.AddModelSession(Model, unit_of_work);
                  context.SaveChanges();

                  transaction.Commit();
               }
               catch (Exception ex)
               {
                  transaction.Rollback();
                  TestBaseCore.mNLogLoggerService.Error(ex.Message);
               }

            }
         }

Is there a better way of optimizing this code, in order to be sure that the connection or the current transaction is still open until all the data it is saved to the database? because when trying to save using this code to a local database everything works perfectly, but when saving to a database hosted by Amazon RDS, the code will crash with no exception.The only difference is the connection string

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