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21 L1LIN Problem
The linearly
constrained L1LIN (
L1LIN) problem is
defined as
|
|
|
|Cx − y)| + alpha*|Lx| |
| subject to |
xL |
≤ |
x |
≤ |
xU |
| |
bL |
≤ |
Ax |
≤ |
bU |
|
(23) |
where
x,
xL,
xU 
Rn,
bL,
bU Rm2,
A
Rm1 × n,
C Rm2 × n,
y
Rm2,
L Rn × b and
alpha R1.
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);
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