Quickguide NLLS Problem

This page is part of the Quickguide Manual. See Quickguide.

The constrained nonlinear least squares (cls) problem is defined as

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} r(x)^T r(x) \\ & \\ s/t & \begin{array}{lcccl} x_{L} & \leq & x & \leq & x_{U}, \\ b_{L} & \leq & A x & \leq & b_{U} \\ c_{L} & \leq & c(x) & \leq & c_{U} \\ \end{array} \end{array} }

where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x, x_L, x_U \in \mathbb{R}^n} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r(x) \in \mathbb{R}^M} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \in \mathbb{R}^{m_1 \times n}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_L,b_U \in \mathbb{R}^{m_1}} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_L,c(x),c_U \in \mathbb{R}^{m_2}} . The following file defines and solves a problem in TOMLAB.

The following files define a problem in TOMLAB.

File: tomlab/quickguide/nllsQG_r.m, nllsQG_J.m

r: Residual vector
J: Jacobian matrix

The following file illustrates how to solve an NLLS problem in TOMLAB. Also view the m-files specified above for more information.

File: tomlab/quickguide/nllsQG.m

Open the file for viewing, and execute nllsQG in Matlab.

 % nllsQG is a small example problem for defining and solving
 % nonlinear least squares using the TOMLAB format.
 Name='Gisela';
 
 t = [0.25; 0.5; 0.75; 1; 1.5; 2; 3; 4; 6; 8; 12; 24; 32; 48; 54; 72; 80;...
      96; 121; 144; 168; 192; 216; 246; 276; 324; 348; 386];
 y = [30.5; 44; 43; 41.5; 38.6; 38.6; 39; 41; 37; 37; 24; 32; 29; 23; 21;...
      19; 17; 14; 9.5; 8.5; 7; 6; 6; 4.5; 3.6; 3; 2.2; 1.6];
    
 x_0 = [6.8729, 0.0108, 0.1248]';
 
 % See help clsAssign for more information.
 Prob = clsAssign('nllsQG_r', 'nllsQG_J', [], [], [], Name, x_0, ...
                  y, t);
 
 % Parameter which is passed to r and J routines.             
 Prob.uP = 5;
 
 Result = tomRun('clsSolve', Prob, 1);
 %Result = tomRun('nlssol', Prob, 1);
 
 % Any nonlinear solver can be used. TOMLAB automatically
 % uses gateway routines for problem mapping.
 
 %Result = tomRun('filterSQP', Prob, 1);
 %Result = tomRun('knitro', Prob, 1);
 %Result = tomRun('conopt', Prob, 1);
 %Result = tomRun('snopt', Prob, 1);
 %Result = tomRun('npsol', Prob, 1);
 %Result = tomRun('minos', Prob, 1);
 %Result = tomRun('oqnlp', Prob, 1);