Algorithmic Methods Used by the Solver

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 Frontline's 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, 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.

Linear Programming

Quadratic Programming

Nonlinear Programming

Mixed-Integer Programming

Copyright © 1996 Frontline Systems Inc.
Last modified: December 01, 1996