InfSolve
Purpose
Find a constrained minimax solution with the use of any suitable TOMLAB solver.
infSolve solves problems of the type:
Failed to parse (unknown function "\multicolumn"): {\displaystyle \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} }
where Failed to parse (unknown function "\Rdim"): {\displaystyle $x,x_L,x_U \in \Rdim{n}$} , Failed to parse (unknown function "\Rdim"): {\displaystyle $r(x) \in \Rdim{N}$} , Failed to parse (unknown function "\Rdim"): {\displaystyle $c(x),c_L,c_U \in\Rdim{m_1}$} , Failed to parse (unknown function "\Rdim"): {\displaystyle $b_L,b_U \in \Rdim{m_2}$} and Failed to parse (unknown function "\Rdim"): {\displaystyle $A \in \Rdim{m_2 \times n}$} .
Calling Syntax
Result=infSolve(Prob,PriLev)
Description of 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. | ||
= 2Standard output from PrintResult (default). |
Description of 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 Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \VAR{J\_k} Failed to parse (syntax error): {\displaystyle }} Failed to parse (unknown function "\VAR"): {\displaystyle \VAR{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 Failed to parse (unknown function "\MATHSET"): {\displaystyle $z\in \MATHSET{R}$} , stored as is added and the problem is rewritten as:
Failed to parse (unknown function "\multicolumn"): {\displaystyle \begin{array}{cccccc} \multicolumn{6}{l}{\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} }
where Failed to parse (unknown function "\Rdim"): {\displaystyle $e \in \Rdim{N},\; e(i)=1 \ \forall i$}
.
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.