Re: Semidefinite programming in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg45151] Re: Semidefinite programming in Mathematica
- From: "Dirk" <dirk.scevenels at skynet.be>
- Date: Thu, 18 Dec 2003 06:55:26 -0500 (EST)
- References: <brci7r$2qe$1@smc.vnet.net> <brfuo6$fdb$1@smc.vnet.net>
- Reply-to: "Dirk" <dirk.scevenels at skynet.be>
- Sender: owner-wri-mathgroup at wolfram.com
Hello Ron, Thanks for your response, although I must admit I do not understand it completely... Are you saying that ANY of the implementations (say, in C) of SDP algorithms are having this precision problem? I'm really not an expert in SDP, I just stumbled upon it in a paper where these methods are used to fit a covariance matrix, and I would like to try this method in Mathematica... So, does anybody know of Mathematica implementations? Or maybe using MathLink to call some C algorithms of SDP? Thanks.... Dirk "Ronald Bruck" <bruck at math.usc.edu> schreef in bericht news:brfuo6$fdb$1 at smc.vnet.net... > In article <brci7r$2qe$1 at smc.vnet.net>, Dirk <dirk.scevenels at skynet.be> > wrote: > > > I've seen some implementations of algorithms related to semidefinite > > programming. > > > > Does anybody know of existing Mathematica implementations? > > Do you mean, in machine precision, or in arbitrary precision? Well, > it's a trick question: no to both. > > Part of the problem here for multiple precision is the need to > implement LAPACK (or parts of it, anyway), especially the Cholesky > decomposition. Unfortunately the LAPACK codebase is replete with > assumptions about double-precision arithmetic, and I don't know of any > implementations which are safe with respect to arbitrary precision. > > Brian Borchers has written a program called CSDP, currently at version > 4.6. I modified Brian's code to do multiprecision arithmetic using the > Gnu Multi-Precision Library, including modifying parts of LAPACK, but > it's based on Brian's version 3.2, and I have no plans to improve to > version 4.6--it's too much of a chore. I've successfully used my code > to do optimizations using real numbers up to 16384 bits in length, but > this isn't of much interest to numerical analysts, because it is SLOW. > (No sense in optimizing the BLAS using ATLAS when a single number takes > up the whole cache!) > > It would be interesting to write a Mathematica interface to my code. > It's somewhere in my list of priorities, but pretty far down. > > If you would like, I can e-mail you my variation of CSDP. Hmmm... I > thought I had put it up on my website, but I don't see it there. Or > much of anything I **thought** was there. Perhaps I can fix this over > the Xmas break. > > --Ron Bruck >