Quickguide MINIMAX Problem - Revision history

Elias at 22:07, 17 January 2012

2012-01-17T22:07:20Z

← Older revision		Revision as of 17:07, 17 January 2012
Line 27:		Line 27:
	Open the file for viewing, and execute minimaxQG in Matlab.		Open the file for viewing, and execute minimaxQG in Matlab.

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% minimaxQG is a small example problem for defining and solving		% minimaxQG is a small example problem for defining and solving
	% minimax programming problems using the TOMLAB format.		% minimax programming problems using the TOMLAB format.
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	Prob.PriLevOpt = 0;		Prob.PriLevOpt = 0;
	Result = tomRun('infSolve', Prob, PriLev);		Result = tomRun('infSolve', Prob, PriLev);
	</~~syntaxhighlight~~>		</source>

Elias at 22:03, 17 January 2012

2012-01-17T22:03:40Z

← Older revision		Revision as of 17:03, 17 January 2012
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	<math>		<math>
	\begin{array}{cccccc} \min\limits_x & ~~\multicolumn{5}{l}~~{\max r(x)} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ & b_L & \leq & Ax & \leq & b_U \\ & c_L & \leq & c(x) & \leq & c_U \\\end{array}		\begin{array}{cccccc} \min\limits_x & {\max r(x)} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ & b_L & \leq & Ax & \leq & b_U \\ & c_L & \leq & c(x) & \leq & c_U \\\end{array}

	</math>		</math>

Elias at 13:32, 10 August 2011

2011-08-10T13:32:49Z

← Older revision		Revision as of 08:32, 10 August 2011
Line 8:		Line 8:
	</math>		</math>

	where <math>x,x_L,x_U \in ~~\Rdim~~{n}</math>, <math>r(x) \in ~~\Rdim~~{N}</math>, <math>c(x),c_L,c_U		where <math>x,x_L,x_U \in R^{n}</math>, <math>r(x) \in R^{N}</math>, <math>c(x),c_L,c_U
	\in ~~\Rdim~~{m_1}</math>, <math>b_L,b_U \in ~~\Rdim~~{m_2}</math> and <math>A \in ~~\Rdim~~{m_2		\in R^{m_1}</math>, <math>b_L,b_U \in R^{m_2}</math> and <math>A \in R^{m_2
	\times n}</math>.		\times n}</math>.

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained minimax''' ('''mima''') problem is defined as
$\begin..."$

2011-08-10T13:18:54Z

Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained minimax''' ('''mima''') problem is defined as <math> \begin..."

New page

{{Part Of Manual|title=the Quickguide Manual|link=[[Quickguide|Quickguide]]}}
The '''constrained minimax''' ('''mima''') problem is defined as 

<math>
\begin{array}{cccccc} \min\limits_x & \multicolumn{5}{l}{\max r(x)} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ & b_L & \leq & Ax & \leq & b_U \\ & c_L & \leq & c(x) & \leq & c_U \\\end{array}

</math>

where <math>x,x_L,x_U \in \Rdim{n}</math>, <math>r(x) \in \Rdim{N}</math>, <math>c(x),c_L,c_U
\in \Rdim{m_1}</math>, <math>b_L,b_U \in \Rdim{m_2}</math> and <math>A \in \Rdim{m_2
\times n}</math>.

The following files define a problem in TOMLAB.

'''File: '''tomlab/quickguide/mimaQG_r.m, mimaQG_J.m

<pre>
r: Residual vector
J: Jacobian matrix
</pre>

The following file illustrates how to solve a minimax problem in TOMLAB. Also view the m-files specified above for more information.

'''File: '''tomlab/quickguide/minimaxQG.m

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

<syntaxhighlight lang="matlab">
% minimaxQG is a small example problem for defining and solving
% minimax programming problems using the TOMLAB format.

Name = 'Madsen-Tinglett 2';
x_0 = [1;1]; % Initial value
x_L = [-10;-10]; % Lower bounds on x
x_U = [10;10]; % Upper bounds on x

% Solve the problem min max |r_i(x)|, where i = 1,2,3
% Solve the problem by eliminating abs, doubling the residuals, reverse sign
% i.e. min max [r_1; r_2; r_3; -r_1; -r_2; -r_3];
y = [-1.5; -2.25; -2.625]; % The data values
y = [y ; -y]; % Eliminate abs, double the residuals, reverse sign
t = []; % No time vector used

%
% Add the linear constraint -x(1) + x(2) + 2 >= 0
% Write the constraint as x(1) - x(2) <= 2

% The A matrix could be specified dense or sparse
% A = sparse([1 -1]);

A = [1 -1];
b_L = -inf;
b_U = 2;

% Generate the problem structure using the Tomlab Quick format
%
% The part in the residuals dependent on x are defined in mima_r.m
% The Jacobian is defined in mima_J.m

Prob = clsAssign('mimaQG_r', 'mimaQG_J', [], x_L, x_U, Name, x_0, y, t, ...
[],[],[],[],A,b_L,b_U);

% Set the optimal values into the structure (for nice result presenting)

Prob.x_opt=[2.3660254038, 0.3660254038];
% Optimal residuals:
r_opt = [0; 0.2009618943;0.375];

% Compute optimal function value:
Prob.f_opt=max(abs(r_opt));

% Use the standard method in infSolve
Prob.InfType = 1;

% Get the default solver
% Solver = GetSolver('con',1,0);

Prob.SolverInf = 'conSolve';

% One may set other solvers:
%Prob.SolverInf = 'snopt';
%Prob.SolverInf = 'npsol';
%Prob.SolverInf = 'minos';
%Prob.SolverInf = 'conSolve';

% Set print level 2 to get output from PrintResult at the end
PriLev = 2;
Prob.PriLevOpt = 0;
Result = tomRun('infSolve', Prob, PriLev);
</syntaxhighlight>

Quickguide MINIMAX Problem - Revision history

Elias at 22:07, 17 January 2012

Elias at 22:03, 17 January 2012

Elias at 13:32, 10 August 2011

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained minimax''' ('''mima''') problem is defined as \begin..."

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained minimax''' ('''mima''') problem is defined as
$\begin..."$