Linear and Nonlinear Programming
A model in which the objective function and all of the constraints (other than integer constraints) are linear functions of the decision variables is called a linear programming (LP) problem. If the objective function or any of the constraints is not a linear function of the decision variables, the model is called a nonlinear programming (NLP) problem. (The term "programming" dates from the 1940s and the discipline of "planning and programming" where these solution methods were first used; it has nothing to do with computer programming.) If the problem includes integer constraints, it is called an integer linear or integer nonlinear programming problem, respectively. A linear programming problem with some "regular" (continuous) decision variables, and some variables which are constrained to integer values, is called a mixed-integer programming (MIP) problem.
A quadratic programming (QP) problem can be thought of as a generalization of a linear programming problem, or as a restricted case of a nonlinear problem. Its objective is a quadratic function of the decision variables, and all of its constraints must be linear functions of the variables. A QP problem cannot be solved with a linear programming "engine" such as the Large-Scale LP Solver. Since a QP problem is a special case of an NLP problem, it can be solved with the standard GRG nonlinear solver in 1-2-3, but this may take far more time than solving an LP of the same size. Frontline's Quadratic Solver includes special methods for efficiently solving QP problems.
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