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30  MAD Problem

TOMLAB /MAD is a package for general automatic differentiation of Matlab code. Usage is applicable for any applications needing derivatives. The package can be used standalone or as part of TOMLAB when floating point precision derivatives are needed.

Following is a simple example of standalone use:

>> x = 1;
>> x = fmad(x,1);
>> y = sin(x);
>> y

value =

    0.8415


derivatives =

    0.5403

An example problem with TOMLAB is included in the guide. The following file defines and solves two problems in TOMLAB.

File: tomlab/quickguide/madQG.m

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

% madQG are two examples for defining and solving nonlinear
% programming problems using TOMLAB /MAD

Name = 'RBB Problem';
x_0 = [-1.2 1]';     % Starting values for the optimization
x_L = [-10;-10];     % Lower bounds for x.
x_U = [2;2];         % Upper bounds for x.
fLowBnd = 0;         % Lower bound on function.

c_L = -1000;         % Lower bound on nonlinear constraints.
c_U = 0;             % Upper bound on nonlinear constraints.

Prob1 = conAssign('rbbQG_f', [], [], [], x_L, x_U, Name, x_0,...
                [], fLowBnd, [], [], [], 'rbbQG_c', [], [], [], c_L, c_U);

Prob2 = conAssign('rbbQG_f', 'rbbQG_g', [], [], x_L, x_U, Name, x_0,...
                [], fLowBnd, [], [], [], 'rbbQG_c', 'rbbQG_dc', [], [], c_L, c_U);

Prob1.Warning = 0;    % Turning off warnings.
Prob2.Warning = 0;    % Turning off warnings.

madinitglobals;
Prob1.ADObj  = 1; % Gradient calculated
Prob1.ADCons = 1; % Jacobian calculated
Result1 = tomRun('snopt', Prob1, 1);  % Only uses first order information.

madinitglobals;
Prob2.ADObj  = -1; % Hessian calculated
Prob2.ADCons = -1; % Lagrangian function for the nonlinear constraints.
Result2 = tomRun('conopt', Prob2, 1);  % Uses second order information.

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