# The OPTQP Procedure

Procedures in Online Documentation

A quadratic programming (QP) problem is identified by a quadratic term (in addition to or without a
linear component) in the objective function and by a collection of linear constraints. Mathematically
the problem can be expressed as follows:

The OPTQP procedure finds the values of variables that minimize the total cost of the solution.
The value of each variable is at or between the variable's lower and upper bounds, and the
constraints are satisfied.

You specify a QP problem in PROC OPTQP by providing the input data as a SAS data set that has a
quadratic programming system (QPS) format. The QPS format is an extension of the widely used
mathematical programming system (MPS) format used for specifying linear programming problems. It includes
an additional section named QSECTION that enables you to specify the Hessian matrix of the quadratic term
in the objective function.

The OPTQP procedure stores the primal and dual output in separate data sets. These data sets contain
problem- and solution-related information. Information related to the problem includes objective function
identification, variable names and types, lower and upper bounds, and so on. Solution-related information
includes the current value of each decision variable and its status in the current solution.

## Examples

OPTQP procedure examples