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The least squares problem
http://forum.alglib.net/viewtopic.php?f=2&t=4573		 Page 1 of 1
Author:  frainbbs2 [ Fri Jul 14, 2023 9:38 am ]
Post subject:  The least squares problem
Dear everyone , dear Sergey :

I have a multi parameter function that needs optimization,

The least squares problem, where F (x, y, z)=ax+by+cz, with coefficients a, b>>c, results in the gradient of z being much smaller than that of a and b. The range of parameters is approximately x [2-5] y [1-3] z [-0.08~0.08]. How to dynamically adjust gradients to improve the accuracy of z

Expand the derivative of z to adjust the scale to be roughly the same as the derivative of x and y?




minbleicstate state;
minbleicreport rep;
double epsg = epsg0 ;
double epsf = epsf0 ;
double epsx = epsx0 ;
ae_int_t maxits = 1000 ; //

minbleiccreate(x, state);
minbleicsetbc(state, bndl, bndu);

//==Is this the order of magnitude for setting parameters related to their coefficients? Is the usage correct here for me?
//real_1d_array xScale;
//int LenS = x.length();
//xScale.setlength(pn);
//int nt_num = LenS/5;
//for(int j=0;j<nt_num;j++){
// xScale[0 * nt_num + j] = 100;
// xScale[1*nt_num+j] = 100 ;
// xScale[2 * nt_num + j] = 1;
// xScale[3*nt_num+j] = 0.5 ;
// xScale[4*nt_num+j] = 0.5 ;
//}
//minbleicsetscale(state,xScale);
//minbleicsetprecscale(state);

minbleicsetcond(state, epsg, epsf, epsx, maxits);
//minbleicoptguardsmoothness(state);
alglib::minbleicoptimize(state, func_grad,NULL,ptr);

//minlmsetacctype(state,1)
const xparams _params = alglib::xdefault;
minbleicrestartfrom(state,x,_params);
minbleicresults(state, x, rep);
Author:  Sergey.Bochkanov [ Sat Jul 15, 2023 10:16 am ]
Post subject:  Re: The least squares problem
Hi!

This specific example is not a problem for BLEIC. The difference in magnitudes is just 10x, first order optimization algorithms can easily deal with differences up to 10000x.

Most often difference in gradient magnitudes comes from different variable scales, so you did it right when you specified scaling with setscale(). It deals with the most part of ill conditioning, and the rest can be handled by the optimizer.

Sergey
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