On solving linear and quadratic programming problems

A simple but effective method for solving linear and quadratic programming problems by solving a set of simultaneous linear equations is presented. The methodology is used to derive an alternative formulation of the linear complementary programming problem, in the context of convex quadratic programming problems, which needs less computational effort than the one formulated by Lemke (1965). In particular, the methodology developed in this paper solves two-variable linear and quadratic integer programming problems elegantly by expressing the solution in terms of at most two parameters. Numerical examples illustrate the solution methodology.