In this paper we consider the general
quadratic programming, which is classified
into: convex quadratic maximization, convex
quadratic minimization and indefinite
quadratic programming. Based on the
optimality conditions (local and global)
we propose algorithms for solving those
problems. The proposed algorithms use linear
programming as subproblems and generate a
sequence of local maximizers or stationary
points. It is shown that the algorithms are
finite and convergent under appropriate
conditions. As applications, some real-world
problems arisen in the response surface, one
of the main topics in the design of
experiment, have been solved numerically by
the algorithms.