An Effective Global Computational Algorithm for a class of Generalized
Linear Multiplicative Programs
This paper explains a region-division-linearization algorithm for
solving a class of generalized linear multiplicative programs (GLMP)
with exponent. In this algorithm, the original non-convex problem (GLMP)
is transformed into a series of linear programming problems by dividing
the outer space of the problem (GLMP) into finite polynomial rectangles.
A new two-stage acceleration technique is put in place to improve the
computational efficiency of the algorithm, which removes part of the
region of the optimal solution without problems (GLMP) in outer space.
In addition, the global convergence of the algorithm is discussed, and
the computational complexity of the algorithm is investigated. It
demonstrates that the algorithm is a completely polynomial time
approximation scheme. Finally, the numerical results show that the
algorithm is effective and feasible.