Optimization Method for Globally Solving a Kind of Multiplicative Problems with Coefficients
Multiplicative problems are a kind of difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, system, finance, economics, and other fields. In this paper, an optimization method is proposed to globally solve a class of multiplicative problems with coefficients. Firstly, by utilizing equivalent transformation and linearization method, a linear relaxation programming problem is established. Secondly, by using branch and bound technique, a determined algorithm is proposed for solving equivalent problem. Finally, the proposed algorithm is convergent to the global optimal solution of original problem by means of the subsequent solutions of a series of linear programming problems.
H. W. Jiao et al., "Optimization Method for Globally Solving a Kind of Multiplicative Problems with Coefficients", Key Engineering Materials, Vols. 467-469, pp. 526-530, 2011