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.