.. _variables-linear_inequality_lower_bounds:

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linear_inequality_lower_bounds
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Define lower bounds for the linear inequality constraint




**Topics**


linear_constraints



.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* REALLIST

- *Default:* vector values = -infinity


**Description**


In the inequality case, the lower :math:`a_l`  and upper :math:`a_u`  bounds provide constraint limits for the two-sided formulation:

.. math:: a_l \leq Ax \leq a_u

Where :math:`A`  is the constrain matrix of variable coefficients.

As with nonlinear inequality constraints (see :dakkw:`responses-objective_functions`), the
default linear inequality constraint bounds are selected so that one-sided inequalities of the form

.. math:: Ax \leq 0.0

result when there are no user bounds specifications (this provides backwards compatibility with previous Dakota versions).

In a user bounds specification, any upper bound values greater than
``+bigRealBoundSize`` (1.e+30, as defined in Minimizer) are treated as
+infinity and any lower bound values less than ``-bigRealBoundSize``
are treated as -infinity.

This feature is commonly used to drop one of the bounds in order to specify a 1-sided constraint (just as the default lower bounds drop out since ``-DBL_MAX`` < ``-bigRealBoundSize``).




**Examples**


Examples of specifying linear inequality constraints to Dakota are
provided on the :dakkw:`variables-linear_inequality_constraint_matrix` page.