Quickguide L1LIN Problem: Difference between revisions
From TomWiki
Jump to navigationJump to search
(Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The linearly '''constrained L1LIN''' ('''L1LIN''') problem is defined as <math> \begin{array}{cccc...") |
No edit summary |
||
Line 4: | Line 4: | ||
<math> | <math> | ||
\begin{array}{cccccc} \min\limits_x & | \begin{array}{cccccc} \min\limits_x & {5}{l}{|Cx - y)| + alpha*|Lx|} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\\end{array} | ||
</math> | </math> | ||
where <math>x,x_L,x_U \in \ | where <math>x,x_L,x_U \in \mathbb{R}^{n}</math>, <math>b_L,b_U \in \mathbb{R}^{m_2}</math>, <math>A\in | ||
\ | \mathbb{R}^{m_1 \times n}</math>, <math>C \in \mathbb{R}^{m_2 \times n}</math>, <math>y \in | ||
\ | \mathbb{R}^{m_2}</math>, <math>L \in \mathbb{R}^{n \times b}</math> and <math>\alpha \in \mathbb{R}^{1}</math>. | ||
The L1Lin solution can be obtained by the use of any suitable linear <span class="roman">TOMLAB</span> solver. | The L1Lin solution can be obtained by the use of any suitable linear <span class="roman">TOMLAB</span> solver. | ||
Line 19: | Line 19: | ||
Open the file for viewing, and execute L1LinQG in Matlab. | Open the file for viewing, and execute L1LinQG in Matlab. | ||
< | <source lang="matlab"> | ||
% L1LinQG is a small example problem for defining and solving | % L1LinQG is a small example problem for defining and solving | ||
% a linearly constrained linear L1 problem using the TOMLAB format. | % a linearly constrained linear L1 problem using the TOMLAB format. | ||
Line 52: | Line 52: | ||
% Prob.SolverL1 = 'CPLEX'; | % Prob.SolverL1 = 'CPLEX'; | ||
% Result = tomRun('L1LinSolve', Prob, 1); | % Result = tomRun('L1LinSolve', Prob, 1); | ||
</ | </source> |
Latest revision as of 18:12, 17 January 2012
This page is part of the Quickguide Manual. See Quickguide. |
The linearly constrained L1LIN (L1LIN) problem is defined as
where , , , , , and .
The L1Lin solution can be obtained by the use of any suitable linear TOMLAB solver.
The following file illustrates how to solve an L1Lin problem in TOMLAB.
File: tomlab/quickguide/L1LinQG.m
Open the file for viewing, and execute L1LinQG in Matlab.
% L1LinQG is a small example problem for defining and solving
% a linearly constrained linear L1 problem using the TOMLAB format.
Name='L1LinSolve test example'; % Problem name, not required.
n = 6;
x_L = -10*ones(n,1); % Lower bounds on x
x_U = 10*ones(n,1); % Upper bounds on x
x_0 = (x_L + x_U) / 2; % Starting point
C = spdiags([1 2 3 4 5 6]', 0, n, n); % C matrix
y = 1.5*ones(n,1); % Data vector
% Matrix defining linear constraints
A = [1 1 0 0 0 0];
b_L = 1; % Lower bounds on the linear inequalities
b_U = 1; % Upper bounds on the linear inequalities
% Defining damping matrix
Prob.LS.damp = 1;
Prob.LS.L = spdiags(ones(6,1)*0.01, 0, 6, 6);
% See 'help llsAssign' for more information.
Prob = llsAssign(C, y, x_L, x_U, Name, x_0, ...
[], [], [], ...
A, b_L, b_U);
Prob.SolverL1 = 'lpSimplex';
Result = tomRun('L1LinSolve', Prob, 1);
% Prob.SolverL1 = 'MINOS';
% Result = tomRun('L1LinSolve', Prob, 1);
% Prob.SolverL1 = 'CPLEX';
% Result = tomRun('L1LinSolve', Prob, 1);