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Linear Constraint Parameters

The following parameters can be passed to the APPSPACK::Constraints::Linear constructor.

Input File Format

If using an input file, these parameters should be in the "Linear" sublist; see Using the APPSPACK Executables. (The use of "Bounds" as the sublist name is also allowed but deprecated.)

Consider the following example constraints:

\[ \begin{array}{ccccc} && x_1 & \leq & 5.7 \\ -0.6 & \leq & x_2 & & \\ 0 & \leq & x_3 & \leq & 1.3 \\ \end{array} \]

\[ \begin{array}{ccc} & x_1 + x_2 + x_3 &\le .1 \\ -4.1 \le & 2x_1 - 9 x_3 & \\ & x_1 - x_2 + x_3 & = -5.2 \\ \end{array} \]

The input file for the "Linear" parameters (see Step 2: Create an APPSPACK input file) is as follows:

@ "Linear"
"Lower" vector 3 DNE -0.6 0
"Upper" vector 3 5.7 DNE 1.3
"Scaling" vector 3 1 1 1
"Inequality Matrix" matrix 2 3
1  1  1
2  0  -9
"Inequality Upper" vector 2 .1    DNE
"Inequality Lower" vector 2 DNE  -4.1
"Equality Matrix" matrix 1 3
1  -1  1
"Equality Bound" vector 1 -5.2
@@

Note that we have explicitly defined "Scaling". This can only be definied implicity if the lower and upper bounds exist for every variable, in which case it is computed as

\[ s_i = u_i - \ell_i \]

where $s_i$ represents the i-th entry of the scaling vector, $u_i$ represents the i-th upper bound, and $\ell_i$ represents the i-th lower bound. Here "DNE" is used to signify that the corresonding bound "Does Not Exist".

See also:
Step 2: Create an APPSPACK input file
Solver Parameters

 

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