Timeline for Mixed integer programming formulation for Ising model
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2014 at 14:57 | history | bounty ended | CommunityBot | ||
| Jul 22, 2014 at 17:18 | comment | added | user40780 | One final remark and question: initially, I don't want to do monte carlo because it could not give a lower bound and upper bound as in integer programming. Do you think this method could provide this bound and the gap would close as computation proceeds? Thank you again very much :) | |
| Jul 22, 2014 at 14:54 | comment | added | user40780 | It's great! Thank you very much again:) But it seems it would be very hard for me to implement it in near future without digging into the formulation......... | |
| Jul 22, 2014 at 14:27 | comment | added | Dmitry Savostyanov | The DMRG / MPS methods arose in quantum physics. The idea was unknown to Maths community for quite some time and was rediscovered under the name Tensor Trains. On this you may wish to check the intro and references in my recent paper 10.1016/j.cpc.2013.12.017 | |
| Jul 22, 2014 at 14:12 | vote | accept | user40780 | ||
| Jul 22, 2014 at 14:11 | comment | added | user40780 | Once again thank you very much:) but do you know what kind of optimization branch in mathematics do they use (is it monte carlo or integer programming)? Or do they start anew solely from condense matter physics? Do you think their methods is general the area of optimization and applicable to the naive looking problem I have? Really thank you very much:) | |
| Jul 22, 2014 at 13:55 | comment | added | Dmitry Savostyanov | They include pairwise interactions, but I doubt it comes to triples. Anyway, the PEPS technique itself is applicable to any interaction pattern. | |
| Jul 22, 2014 at 13:47 | comment | added | user40780 | Uhm... Interesting, I believe they include quadratic terms like s[1,1]*s[1,2], do they also include triplet terms like s[1,1]*s[1,2]*s[2,2]? It's rather difficult for me to infer from their equations, due to different background.... thank you very much :) | |
| Jul 21, 2014 at 23:55 | comment | added | Dmitry Savostyanov | They optimize over wavefunction, which is a linear combination of all possible states, $2^{30 \times 30}$ in your case. You seem to restrict this to pure states only. | |
| Jul 21, 2014 at 22:24 | comment | added | user40780 | So are they really solving exactly the same problem??? with decision variables being the spins and they are trying to minimizing over spin configurations (where spins can only be 0,1)??? Thank you very much:) | |
| Jul 21, 2014 at 22:04 | history | answered | Dmitry Savostyanov | CC BY-SA 3.0 |