Dakota Reference Manual: linear_inequality_constraint_matrix

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linear_inequality_constraint_matrix

Define coefficients of the linear inequality constraints

## Topics

This keyword is related to the topics:

- linear_constraints

## Specification

Alias: none

Argument(s): REALLIST

Default: no linear inequality constraints

## Description

In the inequality case, the constraint matrix provides coefficients for the variables in the two-sided formulation:

Where the bounds are optionally specified by `linear_inequality_lower_bounds`, and `linear_inequality_upper_bounds`. The bounds, if not specified, will default to -infinity, and 0, respectively, resulting in one-sided inequalities of the form

.

The linear_constraints topics page (linked above) outlines a few additional things to consider when using linear constraints.

## Examples

In the first example, an optimization involving two variables, `x1` and `x2`, is to be performed. These variables must satisfy two constraints:

The pair of constraints can be written in matrix form as:

The coefficient matrix and right hand side of this matrix inequality are expressed to Dakota in the variables section of the input file:

    variables
      continuous_design 2
        descriptors 'x1' 'x2'

      linear_inequality_constraint_matrix = 1.5   1.0
                                            1.0  -1.0

      linear_inequality_upper_bounds = 5.0
                                       0.0

The second example is more complex in two respects. First, some, but not all, of the constraints are "two sided", with both lower and upper bounds. Second, not all variables participate in all constraints.

There are four variables, `x1`, `x2`, `x3`, and `x4`, and four constraints.

Or, in matrix form,

The Dakota specification for this matrix inequality is:

    variables
      continuous_design 4
        descriptors 'x1' 'x2' 'x3' 'x4'

      linear_inequality_constraint_matrix = 5.0  2.0  0.0  0.0
                                            1.0  0.0  1.0  0.0
                                            0.0  1.0  0.0  6.0
                                            1.0  1.0  1.0  0.0

      linear_inequality_lower_bounds =  -2.0
                                         0.0
                                        -8.0
                                        -inf

      linear_inequality_upper_bounds = 9.0
                                       inf
                                       8.0
                                       9.0