A method based on parametric convex programming for solving convex multiplicative programming problem

Abstract

We propose a new parametric approach to convex multiplicative programming problem. This problem is nonconvex optimization problem with a lot of practical applications. Compared with preceding methods based on branch-and-bound procedure and other approaches, the idea of our method is to reduce the original nonconvex problem to a parametric convex programming problem having parameters in objective functions. To find parameters corresponding to the optimal solution of the original problem, a system of nonlinear equations which the parameters should satisfy is studied. Then, the system is solved by a Newton-like algorithm, which needs to solve a convex programming problem in each iteration and has global linear and local superlinear/quadratic rate of convergence under some assumptions. Moreover, under some mild assumptions, our algorithm has a finite convergence, that is, the algorithm finds a solution after a finite number of iterations. The numerical results show that our method has much better performance than other reported methods for this class of problems.