Chapter 8 Adaptation to Variational Inequality Problems in Hilbert Spaces
Chapter 8 Adaptive Viscous Algorithm for Variational Inequality Problems in Hilbert Space
Author: Chief Designer
Chapter 8 Adaptive Viscous Algorithm for Variational Inequality Problems in Hilbert Space
Lin Yao's office.
"You kid, I won't deduct your usual points for being late today. It's because you did well in the exam this time."
Lin Yao said to Li Mu who was also in the office.
"Thank you Professor Lin."
Li Mu smiled and said gratefully.
The library was so far away from the classroom, and he didn't have an e-Mule, so he arrived very late. Who would have thought that Professor Lin inside was praising him?
After the next two classes passed, the multivariable calculus class was over.
Then Li Mu was called here by Professor Lin.
Of course, it must be related to this exam.
"Actually, I'm quite curious, why did you suddenly do so well in the exam this time?"
"Uh... maybe I've become enlightened during this period, right?"
Li Mu replied.
Now that there is an extra computer in my mind, it should be considered enlightening, right?
However, Lin Yao did not feel that Li Mu's answer was perfunctory and nodded in agreement: "This is also possible. After all, there are such precedents. Of course, the most important thing is your own talent. You must discover your own talent and make good use of it.
It, this is the best."
Lin Yao is not stingy in his recognition of talent. After all, mathematics is like this. The more talented a person is, the easier it is for him to achieve results, and the more he can promote the development of mathematics.
"So if you have any questions in the future, you can come to me and I can provide you with guidance. If that doesn't work, I can also help you find other teachers. Your first goal is to fully utilize your potential.
."
"Thank you Professor!"
Hearing Lin Yao's words, Li Mu was slightly moved. Just one test score could make him pay so much attention to it, which was enough to show how much Lin Yao valued cultivating students.
Thinking of this, Li Mu hesitated for a moment and thought of the new mission.
Then, he asked: "Professor Lin, I actually have a question for you right now."
"Oh? Just ask." Lin Yao said with a smile.
It was fine if he had questions, he was afraid that Li Mu wouldn't ask.
"I want to write a paper, what topic do you think is better?"
Hearing Li Mu's question, Lin Yao was stunned for a moment, and then laughed.
“Very good, very good.”
As a freshman, I wanted to write a thesis.
Of course, he didn't think Li Mu was too ambitious. He even felt that starting to write papers since his freshman year was something worth promoting.
And such students are also good students that their teachers like!
In response to Li Mu's inquiry, Lin Yao didn't have any secrets and directly listed a lot of topics.
Although Lin Yao is a professor in the School of Mathematics, he also studies physics, so the topics listed are all related to physics and meet Li Mu's needs.
At the same time, Lin Yao spent nearly an hour giving him guidance, including analysis of these topics, recommended books, recommended reviews, papers, etc.
Under Lin Yao's explanation, it can be said that Li Mu quickly understood what he needed to do if he wanted to write a paper from scratch.
You should read the review to understand the research progress of the selected topic, and you should also read the papers in the selected topic, so as to gather the strengths of hundreds of schools and then form a unified opinion.
For Li Mu, who has never written a formal paper, this knowledge requires careful listening.
After all, these are the experiences of a mathematics professor at Shanghai Jiao Tong University.
Until the end, Li Mu saved all the essentials in his mind and said gratefully: "Thank you, Professor."
"You're welcome. I'm a teacher and you're a student. It's my duty to teach you."
Lin Yao smiled and waved his hand, and said: "Then you can go back and find your own topic, and then start writing. If you have any questions, you can ask me. You can also ask prestige."
"Good professor."
Li Mu nodded, then took out his cell phone and added Lin Yao's authority, then stopped disturbing him and left.
Next, he will start working hard for his first paper.
…
It's still a library.
Li Mu opened the GTX960 laptop he bought from his family for more than 3,000 yuan before going to college.
This year is 2019. The 20 series graphics cards have been on the market for half a year, and the 960 has become a treasure from ancient times.
But for him, he can still get through playing LoL, let alone typing and writing a paper.
The only difference from the fruit computers in front of other students in the library is that his notebook is a bit bigger...
Of course, this does not affect the birth of truth.
Create a new folder and name the paper.
Then create a new word document and enter the document interface.
After thinking for a moment, he recalled the topics that Lin Yao had given him just now. Finally, he entered the topics he had decided on.
"Adaptive Viscous Algorithm for Variational Inequality Problems in Hilbert Space"
【Abstract: A new adaptive supergradient is proposed to solve the pseudo-monotone variational inequality problem in Hilbert space. Applying the new step criterion, a strong convergence theorem is obtained without knowing the Lipschitz constant.
The effectiveness of the proposed algorithm is illustrated through some numerical examples.】
This abstract and topic selection were all based on Professor Lin Yao's recommendation and explanation, and then he decided according to his own ideas.
A topic between mathematical physics, or rather, it belongs to the content of [Methods of Mathematical Physics].
And the difficulty of this topic selection...
Li Mu didn't know, but anyway, Lin Yao's evaluation of the original topic was that it was the most difficult of all the topics, and now that he has slightly changed it, he doesn't know how difficult it is.
Probably, it's a little more difficult than the original question?
As for the difficulty in selecting a topic, it mainly lies in Hilbert space.
Hilbert space, one of the core concepts of functional analysis, is also mainly used in formal mathematics and quantum mechanics.
However, during those seventy-two hours, Li Mu had already read all the books on the knowledge points he needed to use, such as functional analysis and quantum mechanics.
Although there is no guarantee that the knowledge points he has now are enough, what needs to be known is that next to him is a library with more than three million books!
If he really encounters a problem, he can get enough knowledge from books. What's more, Professor Lin Yao just recommended several related books to him.
So he didn't worry at all whether the topic was too difficult.
Just like that, he just did it, and then he got ready immediately.
First, he went to borrow books. According to the book list recommended by Professor Lin Yao, he found books that he might be able to use in this paper, and two of them were English textbooks.
Although English textbooks are a bit of a headache, for him now that he has a computer in his mind, learning the language no longer poses any problem. With this kind of English textbook, he can learn both English and the knowledge contained in it.
In addition, there are relevant documents.
In this way, if you don’t understand something, you can look up books and literature, and if you understand something, start writing.
As time passed slowly, he gradually gained a clear understanding of the framework of the entire paper from the knowledge he absorbed, and began to elaborate on the first two parts.
As for the outline, there is no such thing, because he has all these things in his mind.
Time gradually came into the night.
It’s the familiar closing time again.
At least he is very familiar with Li Mu.
After all, he basically ends around this time every night.
Of course, he had paid attention to his time in the past few days, but he had never forgotten it. But today, perhaps he suddenly became obsessed with this kind of high-end problem for him, so that he devoted all his thoughts to it.
Among them, no time was noticed at all.
In this way, the only sound left in the library was the sound of his typing, until about five minutes later, a girl came over.
Yun Rongshang, librarian.
And it was she who reminded Li Mu that the hotel was closed last week night.
This area is the last area she is responsible for. She can simply clean up and leave.
But after arriving here, she couldn't help but admire someone who was still studying seriously.
Anyone who can learn to this extent is worthy of admiration.
But when she saw Li Mu's face, she was stunned.
Isn't this the boy from the physics department last week?
In fact, she came to the library three days a week to take charge, and during these two weeks, she could see Li Mu leaving the library when it was closed.
"Can people really continue to learn like this?"
There are big doubts in my little heart.
What kind of fierce guy is this?
But it seems like this person is writing a thesis now?
She walked forward with some curiosity, took a look, and immediately chose to give up. She was just a finance student and couldn't stand such a thing.
Then he looked at the various books on the desk next to him, such as functional analysis, Hilbert spaces, variational inequalities... and there are even English textbooks?!