# TOMLAB Appendix E

This page is part of the TOMLAB Manual. See TOMLAB Manual. |

## Contents

- 1 External Interfaces
- 1.1 Solver Call Compatible with Optimization Toolbox
- 1.1.1 Table: Call compatible interfaces to MathWorks Optimization TB.
- 1.1.2 Solving LP Similar to Optimization Toolbox
- 1.1.3 Table: Testroutines for the call compatible interfaces to MathWorks Optimization TB present in the
*examples*directory in the TOMLAB distribution. - 1.1.4 Solving QP Similar to Optimization Toolbox

- 1.2 The Matlab Optimization Toolbox Interface
- 1.3 The AMPL Interface

- 1.1 Solver Call Compatible with Optimization Toolbox

## 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. 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.

### 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: Call compatible interfaces to MathWorks Optimization TB. gives a list of the solvers with compatible interfaces.

#### Table: 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: Testroutines for the call compatible interfaces to MathWorks Optimization TB present in the examples directory in the TOMLAB distribution. 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.

#### 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

#### Table: 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. |

**File: **tomlab/usersguide/lpTest2.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/lpTest2.out

linprog (CPLEX): 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: 2 algorithm: 'CPLEX: CPLEX Dual Simplex LP solver' cgiterations: 0 Function value -26.57142857142857300000. ExitFlag 1

#### 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/qpTest2.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/qpTest2.out

Run TOMLAB quadprog on QP Example Constraints Ax-b_U -4.888889e+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: -5.102800e-016 x: 5.555556e-002 5.555556e-002 Output Structure iterations: 1 algorithm: 'qpopt: QPOPT 1.0 QP/LP code' cgiterations: [] firstorderopt: [] Function value -0.02777777777777779000. ExitFlag 1

### The Matlab Optimization Toolbox Interface

Included in TOMLAB is an interface to a number of the solvers in the MathWorks Optimization TB v1.5. and MathWorks Optimization TB. The solvers that are directly possible to use, when a problem is generated in the TOMLAB format, are listed in #Table: Optimization toolbox routines with a TOMLAB interface.. 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: 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. |

### The AMPL Interface

The AMPL interface is described in a separate manual. Enter help amplAssign in MATLAB to see the functionality.