InfSolve: Difference between revisions
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<math> | <math> | ||
\begin{array}{cccccc} | \begin{array}{cccccc} | ||
\min\limits_x & | \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} | \end{array} | ||
</math> | </math> | ||
where <math>x,x_L,x_U \in \ | where <math>x,x_L,x_U \in \mathbb{R}^{n}</math> , <math>r(x) \in \mathbb{R}^{N}</math> , <math>c(x),c_L,c_U \in \mathbb{R}^{m_1}</math> , <math>b_L,b_U \in \mathbb{R}^{m_2}</math> and <math>A \in \mathbb{R}^{m_2 \times n}</math>. | ||
==Calling Syntax== | ==Calling Syntax== | ||
Line 65: | Line 65: | ||
==Description== | ==Description== | ||
The minimax problem is solved in infSolve by rewriting the problem as a general constrained optimization problem. One additional variable <math> | The minimax problem is solved in infSolve by rewriting the problem as a general constrained optimization problem. One additional variable <math>z\in \mathbb{R}</math>, stored as <math>x_{n+1}</math> is added and the problem is rewritten as: | ||
<math> | <math> | ||
\begin{array}{cccccc} | \begin{array}{cccccc} | ||
\min\limits_x z\\\\\mbox{subject to} & x_L & \leq & (x_1,x_2,\ldots,x_n)^T & \leq & x_U \\& -\infty & \leq & z & \leq & \infty \\& b_L & \leq & A x & \leq & b_U \\& c_L & \leq & c(x) & \leq & c_U \\& -\infty & \leq & r(x) - z e & \leq & 0 \\\end{array} | |||
</math> | </math> | ||
where <math>e \in \ | where <math>e \in \mathbb{R}^{N},\; e(i)=1 \ \forall i</math>. | ||
To handle cases where an element <math> | To handle cases where an element <math>r_i(x)</math> in <math>r(x)</math> appears in absolute value: <math>\min \max |r_i(x)|</math>, expand the problem with extra residuals with the opposite sign: <math> [ r_i(x); -r_i(x) ] </math> | ||
==Examples== | ==Examples== |
Revision as of 07:35, 7 December 2011
Purpose
Find a constrained minimax solution with the use of any suitable TOMLAB solver.
infSolve solves problems of the type:
where , , , and .
Calling Syntax
Result=infSolve(Prob,PriLev)
Inputs
Prob | Problem description structure. Should be created in the cls format. infSolve uses two special fields in Prob: | |
---|---|---|
SolverInf | Name of solver used to solve the transformed problem.
Valid choices are conSolve, nlpSolve, sTrustr and clsSolve. If TOMLAB /SOL is installed: minos, snopt, npopt. | |
InfType | 1 - constrained formulation (default).
2 - LS penalty approach (experimental). | |
The remaining fields of Prob should be defined as required by the selected subsolver. | ||
PriLev | Print level in infSolve.
=0 Silent except for error messages. >0 Print summary information about problem transformation. Calls PrintResult with specified PriLev. =2 Standard output from PrintResult (default). |
Outputs
Result | Structure with results from optimization. Output depends on the solver used.
The fields x_k, r_k, J_k, c_k, cJac, x_0, xState, cState, v_k are transformed back to match the original problem. g_k is calculated as J_kT · r_k. The output in Result.Prob is the result after infSolve transformed the problem, i.e. the altered Prob structure |
Description
The minimax problem is solved in infSolve by rewriting the problem as a general constrained optimization problem. One additional variable , stored as is added and the problem is rewritten as:
where .
To handle cases where an element in appears in absolute value: , expand the problem with extra residuals with the opposite sign:
Examples
minimaxDemo.m.
See Also
clsAssign.