Is there a relation between Lagrange multipliers and the difficulty of solving a NLP?

I heard a lot about the interpretation of Lagrange multipliers and the constraints qualification for the resolution of NLP but I still have a question:

Could we qualify the difficulty of solving a NLP based on the values of the Lagrange multipliers at the solutions?

In other words, could we say that a given NLP1 was more difficult to solve that NLP2 if for example max(Lagrange multipliers in 1)> max(Lagrange multipliers in 2)??

This question is motivated by a paragraph talking about sensitivity in the book numerical optimization of Nocedal.

Why are block header bits necessary? (Valid difficulty is already implied by chain history)

Difficulty or target is implied by chain history, so why does it need to be explicit in the header? I suppose it exposes miner-intended-difficulty, but I don’t see why that would be relevant without chain context.

So it seemingly represents redundant data in the header, unless there are any historical reasons for this design choice?

Difficulty appending to cell in Google Sheets

My goal is to automate making a calendar on Google Sheets. I used =DATE(C1,A1,B1) to make a date and then each following cell, I added 1 to the previous cell.

However, now I want to also automate making a time table with this spreadsheet. To append my list of times from below, I used ‘&’, but then the date 12/16/2018 became 43450.

3-4 4-5 5-6 6-7 7-8 8-9 9-10 

What am I overlooking? Any help is appreciated. I am new to Google Sheets, so sorry if this is a stupid question.

How to implement difficulty calculation in my code [duplicate]

This question is an exact duplicate of:

  • How is difficulty calculated for miners?

So let’s say we have to produce a hash that start with “0000”

I hash a block over and over by changing the nonce inside it.

Eventualy I will find a hash that start with “0000”.

What is difficulty here? Is it the ammount of zéros we require the hash to start with? More zero’s would be more difficult? Does it have to do with the nonce?

I understand that the higher the difficulty the more hashes it will take to find it.

If my difficulty is one how do I apply the difficulty in the hashing process.

Right now all im doing is hashihing a block everytime I add 1 to the nonce wich represent the number of hash.

So how do I implement the difficulty in the hash calculation.

I am programming a blockchain from scratch!

Exemple of my code;

generateHash(block) {       let hash = sha256(block.key)       // key contain the block data       while(!hash.startsWith("f07a")) {  // we hash until the hash start with f07a        block.nonce += 1                 // add 1 to nonce for each try        hash = sha256(block.key)         // Trying with the new nonce                 //console.log(hash)                   }       return hash     } 

So how would I implement difficulty here? I know i would have to do more math acording to network hashrate but to understand it in my case how would I use a difficulty of 1 here?