Elias at 22:08, 17 January 2012

2012-01-17T22:08:01Z

← Older revision		Revision as of 17:08, 17 January 2012
Line 4:		Line 4:

	<math>		<math>
	\begin{array}{cccccc} \min\limits_x & ~~\multicolumn{5}{l}~~{\sum_i \|r_i(x)\|} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array}		\begin{array}{cccccc} \min\limits_x & {\sum_i \|r_i(x)\|} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array}
	</math>		</math>

Line 28:		Line 28:
	Open the file for viewing, and execute L1QG in Matlab.		Open the file for viewing, and execute L1QG in Matlab.

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% L1QG is a small example problem for defining and solving		% L1QG is a small example problem for defining and solving
	% an L1 problem using the TOMLAB format.		% an L1 problem using the TOMLAB format.
Line 86:		Line 86:

	Result = tomRun('L1Solve', Prob, PriLev);		Result = tomRun('L1Solve', Prob, PriLev);
	</~~syntaxhighlight~~>		</source>

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained L1''' ('''L1''') problem is defined as $\begin{array}{cccccc} \min\lim..."$

2011-08-10T13:30:24Z

Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained L1''' ('''L1''') problem is defined as <math> \begin{array}{cccccc} \min\lim..."

New page

{{Part Of Manual|title=the Quickguide Manual|link=[[Quickguide|Quickguide]]}}
The '''constrained L1''' ('''L1''') problem is defined as

<math>
\begin{array}{cccccc} \min\limits_x & \multicolumn{5}{l}{\sum_i |r_i(x)|} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array}
</math>

where <math>x,x_L,x_U \in R^n</math>, <math>r(x) \in R^N</math>, <math>c(x),c_L,c_U
\in R^{m_1}</math>, <math>b_L,b_U \in R^{m_2}</math> and <math>A\in R^{m_2
\times n}</math>.

The L1 solution can be obtained by the use of any suitable nonlinear TOMLAB solver.

The following files define a problem in TOMLAB.

'''File: '''tomlab/quickguide/L1QG_r.m, L1QG_J.m

<pre>
r: Residual vector
J: Jacobian matrix
</pre>

The following file illustrates how to solve an L1 problem in TOMLAB. Also view the m-files specified above for more information.

'''File: '''tomlab/quickguide/L1QG.m

Open the file for viewing, and execute L1QG in Matlab.

<syntaxhighlight lang="matlab">
% L1QG is a small example problem for defining and solving
% an L1 problem using the TOMLAB format.

Name = 'Madsen-Tinglett 1';
x_0 = [1;1]; % Initial value
x_L = [-10;-10]; % Lower bounds on x
x_U = [10;10]; % Upper bounds on x

% Solve the problem min max |r_i(x)|, where i = 1,2,3
% Solve the problem by eliminating abs, doubling the residuals, reverse sign
% i.e. min max [r_1; r_2; r_3; -r_1; -r_2; -r_3];
y = [-1.5; -2.25; -2.625]; % The data values
t = []; % No time vector used

% Generate the problem structure using the Tomlab format
% as a standard least squares problem.
%
% The part in the residuals dependent on x are defined in L1ex_r.m
% The Jacobian is defined in L1ex_J.m

Prob = clsAssign('L1QG_r', 'L1QG_J', [], x_L, x_U, Name, x_0, y, t);

% Set JacPattern, L1Solve will compute correct ConsPattern
Prob.JacPattern = ones(length(y),2);

% Set the optimal values into the structure (for nice result presenting)

Prob.x_opt=[3, 0.5];
Prob.f_opt=0;

% Use the standard method in L1Solve
Prob.L1Type = 1;

% Get the default solver
Solver = GetSolver('con',1,0);

Prob.SolverL1 = Solver;

% One may set the solver directly:
%Prob.SolverL1 = 'snopt';
%Prob.SolverL1 = 'npsol';
%Prob.SolverL1 = 'minos';
%Prob.SolverL1 = 'conSolve';

% These statements generate ASCII log files when running SNOPT
if strcmpi(Solver,'snopt')
Prob.SOL.PrintFile = 'snopt.txt';
Prob.SOL.SummFile = 'snopts.txt';
Prob.SOL.optPar(1) = 10; % Print level in SNOPT
%Prob.SOL.optPar(13) = 3; % Verify level in SNOPT
end

% Set print level 2 to get output from PrintResult at the end
PriLev = 2;
Prob.PriLevOpt = 0;

Result = tomRun('L1Solve', Prob, PriLev);
</syntaxhighlight>

Quickguide L1 Problem - Revision history

Elias at 22:08, 17 January 2012

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained L1''' ('''L1''') problem is defined as \begin{array}{cccccc} \min\lim..."

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained L1''' ('''L1''') problem is defined as $\begin{array}{cccccc} \min\lim..."$