| [ KAIST ] in KIDS 글 쓴 이(By): iLUSiON (화려한집념) 날 짜 (Date): 2003년 7월 18일 금요일 오전 07시 41분 43초 제 목(Title): Re: constraint에 대한 질문 하나. probably more explanation is needed since i like my idea of interchaning the objective function to otpimize and constraint function anyway. ^^ Suppose you are solving some electro-magnetic field equation or whatever. For example, if you are sloving \nabla \phi = 0 with some boundary constrain g(\phi) = 0, where \nabla is Laplacian. now suppose the boundary of your domain is extreamly complicated and no analytical soluation is possible. Then a reasonable numerical solution can be obtained via the finite element method (FEM) by triangulating the complex domain. If you are minimizing F with constraint G, you use variational principle to change it to the partial differential equations. Solving PDE via FEM is trivial if your PDE operators are self-adjoint. If not, well you can still do it by solving huge linear system iteratively. Formulating FEM and writing computer codes real SUX big time! it is no-ga-da suitable to gong-do-ris but not to scientists who are too busy to think something nobel. ;) now here comes our great Monte-carlo. this is extreamly innocent looking very strange concept. It was only possible when computer was invented in 1940's for military research. The concept is due to Von Neumann and a physicists Kosh (my memory is somewhat fuzzy in this regard due to too much of womenizing. ^^) in relation to random walk. then came the idea of resampleing (bootstraping) in 70's. since then computational statistics became a major nemrical tools for almost all area of science and engineering where analytical solution is hard to get by. why would you spend 1000 hours trying to get exact analystical solution when if you spend 10 hours fomulating Monte-carlo and get very good approximation. there are many ways to speed up Monte-carlo convergence so the accuracy or computational time is not a problem. this is what we statisticans call 'simulation'. so instead of hiring 10 gong-so-ris to solve a problem for 1000 hours, hire a good computiontion oriented statistian to solve it in 10 hours. good for your buck and your research fudning. ;) ok let's get to the point instead of gong-do-ri bashing. but it is always fun isn't it. hehe... MC is superb when optimization function F is simple while constraint are nightmarish complicated G. but in Lina's problem, F is complicated while G is simple. well who cares about interchaning F and G. just pretend F is your constraint then and G to be your objective function to minimize and solve your Lagrangi(? man... arrrr french spelling i can't get it correct even thou i spend a couple of years in montreal). WHY? F + hG = h(1/hF + G). so make 1/h to be your Lagrange (oh ya.. i got it correct hehehehe..so happy ^^) and do MC to this setting. cool? iLUSiON whitepolarcow@hotmail.com |