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E External Interfaces
Some users may have been used to work with MathWorks Optimization
Toolbox, or have code written for use with these toolboxes. For that
reason TOMLAB contains interfaces to simplify the transfer of code to
TOMLAB . There are two ways in which the MathWorks Optimization
Toolbox may be used in TOMLAB . One way is to use the same type of call
to the main solvers as in MathWorks Optimization TB, but the solution is obtained by
converting the problem into the TOMLAB format and calling a TOMLAB solver. The
other way is to formulate the problem in any of the TOMLAB formats,
but when solving the problem calling the driver routine with the
name of the Optimization Toolbox solver. Interfaces have been made
to both MathWorks Optimization TB and MathWorks Optimization TB v1.5. Which way to use is determined by setting
if 0 or
if 1 in
startup.m in the addpath for the
variable
OPTIM . If setting
if 1 then the TOMLAB versions
are put first and MathWorks Optimization TB is not accessible.
E.1 Solver Call Compatible with Optimization
Toolbox
TOMLAB is call compatible with MathWorks Optimization TB. This means that the same syntax
could be used, but the solver is a TOMLAB solver instead. TOMLAB
normally adds one extra input, the
Prob structure, and one
extra output argument, the
Result structure. Both extra
parameters are optional, but if the user are adding extra input
arguments in his call to the MathWorks Optimization TB solver, to use the TOMLAB
equivalents, the extra input must be shifted one step right, and the
variable
Prob be put first among the extra arguments. Table
32 gives a list of the solvers with compatible
interfaces.
Table 32: Call compatible interfaces to MathWorks Optimization TB.
|
| Function |
Type of problem solved |
|
| bintprog |
Binary programming. |
| fmincon |
Constrained minimization. |
| fminsearch |
Unconstrained minimization using Nelder-Mead type simplex search method. |
| fminunc |
Unconstrained minimization using gradient search. |
| linprog |
Linear programming. |
| lsqcurvefit |
Nonlinear least squares curve fitting. |
| lsqlin |
Linear least squares. |
| lsqnonlin |
Linear least squares with nonnegative variable constraints. |
| lsqnonneg |
Nonlinear least squares. |
| quadprog |
Quadratic programming. |
|
In Table
33 a list is given with the
demonstration files available in the directory
examples
that exemplify the usage of the call compatible interfaces. In the
next sections the usage of some of the solvers are further
discussed and exemplified.
Table 33: Testroutines for the call compatible interfaces to MathWorks Optimization TB present
in the examples directory in the TOMLAB distribution.
|
| Function |
Type of problem solved |
|
| testbintprog |
Test of binary programming. |
| testfmincon |
Test of constrained minimization. |
| testfminsearch |
Test of unconstrained minimization using
a Nelder-Mead type simplex search method. |
| testfminunc |
Test of unconstrained minimization using gradient search. |
| testlinprog |
Test of linear programming. |
| testlsqcurvefit |
Test of nonlinear least squares curve
fitting. |
| testlsqlin |
Test of linear least squares. |
| testlsqnonlin |
Test of linear least squares with nonnegative variable constraints. |
| testlsqnonneg |
Test of nonlinear least squares. |
| testquadprog |
Test of quadratic programming. |
|
E.1.1 Solving LP Similar to Optimization Toolbox
For linear programs the MathWorks Optimization TB solver is
linprog .
The TOMLAB
linprog solver adds one extra input argument, the
Prob structure, and one extra output argument, the
Result structure. Both extra parameters are optional, but
means that the additional functionality of the TOMLAB LP solver is
accessible.
An example of the use of the TOMLAB
linprog solver
to solve test problem
(
13) illustrates the basic usage
File: tomlab/usersguide/lpTest4.m
lpExample;
% linprog needs linear inequalities and equalities to be given separately
% If the problem has both linear inequalities (only upper bounded)
% and equalities we can easily detect which ones doing the following calls
ix = b_L==b_U;
E = find(ix);
I = find(~ix);
[x, fVal, ExitFlag, Out, Lambda] = linprog(c, A(I,:),b_U(I),...
A(E,:), b_U(E), x_L, x_U, x_0);
% If the problem has linear inequalites with different lower and upper bounds
% the problem can be transformed using the TOMLAB routine cpTransf.
% See the example file tomlab\examples\testlinprog.m for an example.
fprintf('\n');
fprintf('\n');
disp('Run TOMLAB linprog on LP Example');
fprintf('\n');
xprinte(A*x-b_U, 'Constraints Ax-b_U ');
xprinte(Lambda.lower, 'Lambda.lower: ');
xprinte(Lambda.upper, 'Lambda.upper: ');
xprinte(Lambda.eqlin, 'Lambda.eqlin: ');
xprinte(Lambda.ineqlin, 'Lambda.ineqlin: ');
xprinte(x, 'x: ');
format compact
disp('Output Structure')
disp(Out)
fprintf('Function value %30.20f. ExitFlag %d\n',fVal,ExitFlag);
The results from this test show the same results as previous runs
in Section
5, because the same solver is called.
File: tomlab/usersguide/lpTest4.out
linprog (MINOS): Optimization terminated successfully
Run TOMLAB linprog on LP Example
Constraints Ax-b_U 0.000000e+000 0.000000e+000
Lambda.lower: 0.000000e+000 0.000000e+000
Lambda.upper: 0.000000e+000 0.000000e+000
Lambda.eqlin:
Lambda.ineqlin: -1.857143e+000 -1.285714e+000
x: 2.571429e+000 1.714286e+000
Output Structure
iterations: 1
algorithm: 'MINOS: MEX-interface to MINOS 5.5 NLP code'
cgiterations: 0
Function value -26.57142857142856600000. ExitFlag 1
E.1.2 Solving QP Similar to Optimization Toolbox
For quadratic programs the MathWorks Optimization TB solver is
quadprog . The TOMLAB
quadprog solver adds one extra
input argument, the
Prob structure, and one extra output
argument, the
Result structure. Both extra parameters are
optional, but means that the additional functionality of the TOMLAB
QP solver is accessible.
An example of the use of the TOMLAB
quadprog solver
to solve test problem
(
15) illustrates the basic usage
File: tomlab/usersguide/qpTest4.m
qpExample;
% quadprog needs linear equalities and equalities to be given separately
% If the problem has both linear inequalities (only upper bounded)
% and equalities we can easily detect which ones doing the following calls
ix = b_L==b_U;
E = find(ix);
I = find(~ix);
[x, fVal, ExitFlag, Out, Lambda] = quadprog(F, c, A(I,:),b_U(I),...
A(E,:), b_U(E), x_L, x_U, x_0);
% If A has linear inequalites with different lower and upper bounds
% the problem can be transformed using the TOMLAB routine cpTransf.
% See the example file tomlab\examples\testquadprog.m for an example.
fprintf('\n');
fprintf('\n');
disp('Run TOMLAB quadprog on QP Example');
fprintf('\n');
xprinte(A*x-b_U, 'Constraints Ax-b_U ');
xprinte(Lambda.lower, 'Lambda.lower: ');
xprinte(Lambda.upper, 'Lambda.upper: ');
xprinte(Lambda.eqlin, 'Lambda.eqlin: ');
xprinte(Lambda.ineqlin, 'Lambda.ineqlin: ');
xprinte(x, 'x: ');
format compact
disp('Output Structure')
disp(Out)
fprintf('Function value %30.20f. ExitFlag %d\n',fVal,ExitFlag);
The restricted problem formulation in MathWorks Optimization TB
sometimes makes it necessary to transform the problem.
See the comments in the above example and the test problem file
tomlab/examples/testquadprog.m
.
The results from this test show the same results as previous runs
File: tomlab/usersguide/qpTest4.out
Run TOMLAB quadprog on QP Example
Constraints Ax-b_U -4.900000e+000 0.000000e+000
Lambda.lower: 0.000000e+000 0.000000e+000
Lambda.upper: 0.000000e+000 0.000000e+000
Lambda.eqlin: -3.500000e+000
Lambda.ineqlin: 0.000000e+000
x: 5.000000e-002 5.000000e-002
Output Structure
iterations: 1
algorithm: 'bqpd: MEX-interface to BQPD QP/LP code'
cgiterations: []
firstorderopt: []
Function value -0.02500000000000000100. ExitFlag 1
E.2 The Matlab Optimization Toolbox Interface
Included in TOMLAB is an interface to a number of the solvers in the
MathWorks Optimization TB v1.5
[
12].
and MathWorks Optimization TB
[
14].
The solvers that are directly possible to
use, when a problem is generated in the TOMLAB format,
are listed in Table
34.
The user must of course have a valid license.
The TOMLAB interface routines are
opt15Run and
opt20Run , but
the user does not need to call these directly, but can use the
standard multi-solver driver interface routine
tomRun .
Several low-level interface routines have been written.
For example, the
constr solver needs both the
objective function and the vector of constraint functions in the same call,
which
nlp_fc supplies. Also the gradient vector and the matrix of
constraint normals should be supplied in one call. These parameters are
returned by the routine
nlp_gdc .
MathWorks Optimization TB v1.5
is using a parameter vector OPTIONS of length 18, that the routine
foptions is setting up the default values for.
MathWorks Optimization TB is instead using a structure.
Table 34: Optimization toolbox routines with a TOMLAB interface.
|
| Function |
Type of problem solved |
|
| bintprog |
Binary programming. |
| fmincon |
Constrained minimization. |
| fminsearch |
Unconstrained minimization using Nelder-Mead type simplex search method. |
| fminunc |
Unconstrained minimization using gradient search. |
| linprog |
Linear programming. |
| lsqcurvefit |
Nonlinear least squares curve fitting. |
| lsqlin |
Linear least squares. |
| lsqnonlin |
Linear least squares with nonnegative variable constraints. |
| lsqnonneg |
Nonlinear least squares. |
| quadprog |
Quadratic programming. |
| constr |
Constrained minimization. |
| fmins |
Unconstrained minimization using Nelder-Mead type simplex search method. |
| fminu |
Unconstrained minimization using gradient search. |
| leastsq |
Nonlinear least squares. |
| lp |
Linear programming. |
| qp |
Quadratic programming. |
|
E.3 The AMPL Interface
The AMPL interface is described in a separate manual. Enter help
amplAssign in MATLAB to see the functionality.
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