The Quadratic Programming Solver -- Experimental |

The OPTMODEL procedure provides a framework for specifying and solving quadratic programs.

Mathematically, a quadratic programming (QP) problem can be stated as follows:

is the quadratic (also known as Hessian) matrix | ||||

is the constraints matrix | ||||

is the vector of decision variables | ||||

is the vector of linear objective function coefficients | ||||

is the vector of constraints right-hand sides (RHS) | ||||

is the vector of lower bounds on the decision variables | ||||

is the vector of upper bounds on the decision variables |

The quadratic matrix is assumed to be symmetric; i.e.,

In addition to being symmetric, is also required to be positive semidefinite:

**Figure 12.1:** Examples of Convex, Concave, and Nonconvex Objective Functions

The order of constraints is insignificant. Some or all components of or (lower/upper bounds) can be omitted.

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