mm-22657 Subject: Global Optimization How do you implement local minimisation methods to find the global minimum of a function? === Subject: Re: Global Optimization >How do you implement local minimisation methods to find the global >minimum of a function? combine with branch and bound. http://plato.la.asu.edu/topics/problems/global.html http://www.mat.univie.ac.at/~neum/software/ hth peter === Subject: Re: Global Optimization Write your problem as a posynomial and it will have only one solution. A local method could solve it. Reference Geometric Programming to find out more about posynomial representations. Paul > How do you implement local minimisation methods to find the global > minimum of a function? > How do you implement local minimisation methods to find the global > minimum of a function? === Subject: Re: qr update and leastsquares > Note that for fixed A but multiple u,v,b, the expensive step (1) needs to be > done only once, whereas the cheap steps (2)-(6) must be done repeatedly. > Therefore, this is very efficient. that, but my calculations are cleary not as fast as yours... Can you just give me a hint on the origin af such solutions ? (is it classic, and if it is are there any pointers were I could check on that ?). Anyway > as solution of the original problem. If some diagonal elements of D are > tiny, the problem is poorly posed and must be suitably regularized. I usually do this by zeroing the small singular values when inversing the diagonal. It could be done once only with your algorithm. I guess it is possible to do better. I'll take a look on that. -- Jerome === Subject: Re: qr update and leastsquares > Note that for fixed A but multiple u,v,b, the expensive step (1) needs to be > done only once, whereas the cheap steps (2)-(6) must be done repeatedly. > Therefore, this is very efficient. > Can you just give me a hint on the origin af such solutions ? 1. Solving a rank one modification of a linear system is standard (Shermann-Morrison). 2. SVD can be viewed as a transformation to a simple normal form. Doing the transformation simplifies the solution of the rank one modifications. Where does your problem come from? Arnold Neumaier === Subject: Re: qr update and leastsquares > 1. Solving a rank one modification of a linear system is standard > (Shermann-Morrison). > 2. SVD can be viewed as a transformation to a simple normal form. > Doing the transformation simplifies the solution of the rank one > modifications. I knew 1 and 2 but could not put them together. I was in my QR trip, but huge multi-colinearities stopped me ;-) > Where does your problem come from? I am modelling surfaces from datas observed with a generalised linear model where my expansions depend on 3 parameters. The dependance on one of them (the two others being fixed) lead to rank-one modification, so finding each step of the expansion the best new basis function follows the problem I submitted to the forum. In fact my model is very close/inspired from Friedmann's MARS model. It is very likely that I am reinventing the wheel here ;-) -- Jerome === Subject: Re: qr update and leastsquares >No the first one. Meaning you have a collection of {u_i,v_i}, A and b fixed, >and you need to solve many (A+u_i*v_i')x=b. I ran across this reference this evening: L. Reichel , W. B. Gragg, Algorithm 686: FORTRAN subroutines for updating the QR decomposition, ACM Transactions on Mathematical Software (TOMS), v.16 n.4, p.369-377, Dec. 1990 I know nothing about it (I was looking for something unrelated), but figured it looked interesting enough to add to your to.read list. === Subject: Re: Small sample size and logit model >I have a sample of 6 observations and due to the conditions I cannot >make it bigger. Can I use any statistical models for such a sample? I >donot want to make a prediction, I just want to describe the past >period for wihch I have data. Can I use regresion? Can I use logit? >Perhaps you can recommend some books where this issue would be >discussed (small sample size, but I am NOT a mathematician, so I need >a rather easy-to-read book). in the extreme case, with 6 parameters (what is logit?) you might desribe the six data points exactly, neglecting the data errors. the rule of thumb is sqrt(of number of data points/2)>=number of parametrs. here : 1, maybe 2. software: see http://plato.la.asu.edu/topics/problems/nlolsq.html hth peter === Subject: Re: making a symmetric matrix positive definite -- Bobby Cheng The MathWorks, Inc. http://www.mathworks.com >> Given the Hessian, H, of a function f: R^n -> R, if H is not pd, and we >> would like to do something like H* = H + cI, to make H* pd, is there a way >> to get the information needed from the LAPACK Cholesky routines >> (specifically, dpptrf) to make an estimate of what c needs to be >Hm. You could look at the first negative pivot, and add that much to the >diagonal. That doesn't guarrantee you that on re-factoring you won't get >a negative pivot later, but you could repeat this process. >You could also take the Gershgorin circle theorem, and add so much to >the diagonal that the matrix becomes diagonally dominant. It may not be >the minimal amount, but it's guaranteed. >V. >-- >mail me at lastname at cs utk edu > J.J. {textsc{Mor'{e}}} and D.C. {textsc{Sorensen}}. > newblock Computing a trust region step. > 4(3):553--572, 1983. > use a linpack routine to estimate the smallest eigenvalue and they use > information from the Cholesky factorization. This arises in their > safeguarding routine > i.e. they need to guarantee that H+cI is positive definite > in their safeguarding during the algorithm for TRS. > -- > Prof. Henry Wolkowicz |Email: hwolkowicz@uwaterloo.ca > Univ. of Waterloo |URL http://orion.math.uwaterloo.ca/~hwolkowi > Dept of Comb and Opt |Tel (519) 888-4567, x5589, office MC6065 > Waterloo, Ont. CANADA N2L 3G1 |Fax (519) 725-5441 === Subject: about spectral method I am not quite familiar with spectral method. I know that when Spectral method is applied, we have to consider the problem in frequency domain. However, the numerical fourier transformation will lead to some error which is in complex form and in the time doamin it's something like a oscillating wave. I wonder how to absorb the oscillating wave and keep the numberical result as accurate as possible. === Subject: Re: Does anyone use functional programming languages > I wonder why functional programming languages like Objective Caml or SISAL > are still completely unknown to scientists. > They are extremely good (if not much better) alternatives to Fortran and > C++, in terms of expressive power, easiness, and safety, and their > performance is known to be comparable with C. > Yet Fortran is still taught to physics students like it was the alpha and > the omega of numerical programming. Why is it so ? Snapshot of projects in freshmeat.net (9/27/03) by programming language count. 22 projects (out of about 19000) list Caml. Fortran count is 45. Programming Language * Ada (38 projects) * APL (3 projects) * ASP (26 projects) * Assembly (177 projects) * Awk (40 projects) * Basic (15 projects) * C (5517 projects) * C# (45 projects) * C++ (2481 projects) * Cold Fusion (10 projects) * Common Lisp (29 projects) * Delphi (50 projects) * Dylan (2 projects) * Eiffel (21 projects) * Emacs-Lisp (33 projects) * Erlang (11 projects) * Euler (1 project) * Euphoria (2 projects) * Forth (16 projects) * Fortran (45 projects) * Haskell (28 projects) * Java (2396 projects) * JavaScript (235 projects) * Lisp (66 projects) * Logo (2 projects) * ML (26 projects) * Modula (7 projects) * Object Pascal (10 projects) * Objective C (136 projects) * OCaml (22 projects) * Other (163 projects) * Other Scripting Engines (85 projects) * Pascal (38 projects) * Perl (2764 projects) * PHP (2060 projects) * Pike (3 projects) * PL/SQL (61 projects) * Pliant (1 project) * PROGRESS (2 projects) * Prolog (8 projects) * Python (1198 projects) * Rexx (7 projects) * Ruby (128 projects) * Scheme (79 projects) * Simula (1 project) * Smalltalk (21 projects) * SQL (293 projects) * Tcl (357 projects) * Unix Shell (554 projects) * Visual Basic (15 projects) * XBasic (1 project) * YACC (11 projects) * Zope (34 projects) === Subject: question about 3d plottin software data table limit Hy, I have a quite noise problem, by a wavelet analysis I've obtained a data table of frequency, time and energy, the problem is that the table is very long (3 columns and somthing like 13 milion of rows) I need to plot this table in a 3d graphic, but at now I don't find a program (quite simple to use) that has a so high limit in is data table lenght (usually are of 2^15 or 2^16 of rows). Do you know is exist a program with a no limit data table lenght? Also a shareware or trial version is good to me. Kio === Subject: Computational Evolution without velocities I have heard the folklore that when one wants to simulate some structure Newton's laws (i.e. non-relativistic) one can neglect the fact that the update formula x_new = x_old - Force DeltaTime / 2 Mass holds for any simulation and we do not need to take care of velocities. What I would like to know is does anyone know whether this holds only under certain conditions (evolution at equilibrium, etc.) and/or knows of research papers that deal with this issue and perhaps give a proof of this claim as a theorem. The strange thing is that apparently this is very well known and widely practised but no one I've spoken to knew where to find the details. Pat Free your mind. There is no spoon. ************************************************ Dr. Patrick Bangert http://www.knot-theory.org Research Instructor for Mathematics International University Bremen === Subject: Re: Computational Evolution without velocities === >Subject: Computational Evolution without velocities >I have heard the folklore that when one wants to simulate some structure >Newton's laws (i.e. non-relativistic) one can neglect the fact that the >update formula >x_new = x_old - Force DeltaTime / 2 Mass >holds for any simulation and we do not need to take care of velocities. What >I would like to know is does anyone know whether this holds only under >certain conditions (evolution at equilibrium, etc.) and/or knows of research >papers that deal with this issue and perhaps give a proof of this claim as a >theorem. The strange thing is that apparently this is very well known and >widely practised but no one I've spoken to knew where to find the details. >Pat I expect this is some version of the fact that when simulating physical systems subject to various conservation laws it may not be possible to exactly satisfy all of them, particularly when doing something like using quantized (discrete) coordinates. In that case one should consciously (rather than by computational/programming accident) choose which ones to satisfy. Some time ago there were galactic evolution simulations which preserved virial and anglular momentum but were only close on the equations of motion and energy (they were monitored and stayed sensible). The results seemed to make sense to the folks doing them. This observations may well lead to the sort of folklore you suggest and it may be questionable whether the reduction is accurrate or misleading. Folklore is always prone to misunderstanding as it lacks its context. The very old citations I would have are to Richard Miller of Univ of Chicago. >Free your mind. There is no spoon. >************************************************ >Dr. Patrick Bangert >http://www.knot-theory.org >Research Instructor for Mathematics >International University Bremen