When I realized semidefinite programming is applicable to 2-RDM theory?

In 1996 or so, Prof. Nakatsuji and Yasuda solved the density equation after Valdemoro and co-wokers solved it (she calls as contracted Schroedinger equation). This is a great achivement and I was at bachelor student at Kyoto Univ. Yasuda-san got Ph.D in this year so our overlap is only one year. What a pity.
What I did in the first year - very simple extension - just describe openshell system, and nothing has been changed in the theory. I could determine some systems like H2O, Be, etc after three years, nothing more. Density equation is very unstable. I was really disappointing about it and something I should change the way I do. At first Nakatsuji-sensei was not happy with my change, of course, he found the density equation (or contracted schroedinger equation).

I read many older papers. Garrod, Fusco, Mihailovic, Rosina, Kijiwski are the early pioneers to trying to variational calculation, and surprisingly, their results for Be are very promising. So I decided to do variational calculation. All papers are quite pessimistic about P, Q, and G conditions. Yes, I know it. However, only two papers at the three years makes me crazy. I thought that I can reproduce Be result, and at least I know by Kummer's paper or Erdahl's paper that P Q G are compact (in what sense?) and Hamiltonian is linear functional, so we have at least well-defined minima (yes we can have results! if there are no numerical issues). also G-condition is somewhat related to BCS type wavefunction, I hoped that it can apply to some systems.

At that time I thought that I can reproduce Be result, but may fail for larger systems like H2O
but _AT LEAST_ I can get 2-RDMs (compactness of P,Q,Gdomain and if not numerical issues) and publish a paper! Oh what a joy!

In 1999/3/30, I asked at fj.sci.math about optimization of linear functional over semidefinite constraint. Ono-san kindly replied as there is an established field in mathematical programming and some implementations are available via internet. Kojima-lab is the one of the active lab in Japan.

So I started. I read many Prof.Kojima's resumes but I just understand semi-definite programming can be used for variational 2-RDM.

I e-mailed to Mituhiro Fukuda, now he's my friend, about it. I proposed him a very simplified problem and he kindly show me how to translate it to "primal" standard type problem.

It took only one month to understand how I "play" with SDPA. Implementation was a breeze. With P and Q condition, Be energy was -17 au or something, and it is expected :)

Incorporating G-condition was really tough. Really exhausted. I tried, tried and tried. all are my stupid bugs, and misunderstanding of SDP or something like that.

Finally I got some results until fall. I fixed the final stupid bug. Then I got many results. Lab seminar was held at 99/12/7, I presented some results. I was very happy about it. and
Nakatsuji-sensei told me "this is a very important result". it was my great pleasure!!

This result was published as JCP 2001.
After I submitted a manuscript, referee comment was very affirmative. However, due to
my laziness, I just left for a while. Nakatsuji-sensei scold me. If I were bit more smart, it was
published in 2000.