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Literature on financial optimization, in particular on the method of critical lines of Markowitz?
UPD : I realized my mistake, not everyone is familiar with finance and Markowitz :)
I will explain more formally. I want to learn how to solve quadratic parametric programming problems with linear constraints (parameter takes values [1;infinity)). Formally, it comes down to finding a finite number of corner points and obtaining an effective front by linear interpolation between them. My gap is just in finding these corner points. A simple detailed example (preferably not in matrix form) or an article / book that does not go into the jungle will be enough for me.
The original question is below:
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I've been trying to figure out how to build an efficient stock portfolio for months now and can't figure out the critical lines method. I am not a mathematician and I am familiar with something higher than the school curriculum solely in connection with the enormous interest I have (I did not study systematically, only directions that were interesting to me at an amateur level). I tried to study optimization and at this stage I can solve simple quadratic programming problems, but all attempts to find information using the critical line method come down to A.S. Shvedov, where mathematics is beyond my understanding.
Could you, if possible, advise literature on this issue or a person with whom it can be discussed?
In order to understand my level, I cite the literature with which I got acquainted before writing here:
- Mathematical programming in examples and tasks (Akulich I.L. ed. Higher School, 1986): I can solve the ZNP by the Lagrange method and the sign with linear programming (including parametric programming, only the transport problem did not submit to me ...). In this context, "can" means that I solved the simplest tasks that are given in the textbook.
- Boss lectures on optimization: I tried to understand the Kuhn-Tucker theorem from the book, but I didn’t figure out the proof, which doesn’t prevent it from being used when solving the ZNP, but it’s just a shame :)
- I tried to read A.S. Shvedov (a manual on the theory of efficient portfolios of securities), but the mathematics there are the last two chapters, which describe the algorithms of interest to me beyond my understanding. After reading everything that is stated above - I understood a little less than nothing.
I will be grateful if you direct me in the direction where I can deal with the method of critical lines. Perhaps someone has preserved lectures, or someone will be so kind and explain all this to me on the fingers.
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